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AIAA-2002-2743

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American Institute of Aeronautics and Astronautics

BOUNDARY LAYER TRANSITION ON SLENDER CONES IN CONVENTIONALAND LOW DISTURBANCE MACH 6 WIND TUNNELS

Thomas J. Horvath∗, Scott A. Berry∗, Brian R. Hollis∗⊕

Chau-Lyan Chang✝ ⊕, and Bart A. Singer✝ ⊕

NASA Langley Research Center

AbstractAn experimental investigation was conducted on a 5-degree half-angle cone and a 5-degree half-angle flared

cone in a conventional Mach 6 wind tunnel to examine the effects of facility noise on boundary layer transition. Theinfluence of tunnel noise was inferred by comparing transition onset locations determined from the present test tothat previously obtained in a Mach 6 low disturbance quiet tunnel. Together, the two sets of experiments arebelieved to represent the first direct comparison of transition onset between a conventional and a low disturbancewind tunnel using a common test model and transition detection technique. In the present conventional hypersonictunnel experiment, separate measurements of heat transfer and adiabatic wall temperatures were obtained on theconical models at small angles of attack over a range of Reynolds numbers, which resulted in laminar, transitional,and turbulent flow. Smooth model turbulent heating distributions are compared to that obtained with transitionforced via discrete surface roughness. The model nosetip radius was varied to examine the effects of bluntness ontransition onset. Despite wall-to-total temperature differences between the transient heating measurements and theadiabatic wall temperature measurements, the two methods for determining sharp cone transition onset generallyyielded equivalent locations. In the “noisy” mode of the hypersonic low disturbance tunnel, transition onset occurredearlier than that measured in the conventional hypersonic tunnel, suggesting higher levels of freestream acousticradiation relative to the conventional tunnel. At comparable freestream conditions, the transition onset Reynoldsnumber under low disturbance conditions was a factor of 1.3 greater than that measured on flared cone in the LaRCconventional hypersonic tunnel and a factor of 1.6 greater than the flared cone run in the low disturbance tunnel run“noisy”. Navier-Stokes mean flow computations and linear stability analysis were conducted to assess theexperimental results and have indicated N factors associated with sharp flared cone transition onset to beapproximately a factor of 2 lower than that inferred from the corresponding low disturbance tunnel measurements.

Nomenclatureh heat transfer coeff. (lbm/ft2-sec), q/(Haw- Hw)

where Haw = Ht,2

H enthalpy (BTU/lbm)k boundary layer trip height (in.)L reference length based on sharp tip model (in)M Mach numberN exponential factor in amplification ratio eN

from linear stability theoryP pressure, psiaq heat transfer rate (BTU/ft2-sec)R or r radius (in.)t time (sec)Re unit Reynolds number (1/ft)T temperature (°F)x axial distance from cone apex (in.)

∗Aerothermodynamics Branch, NASA Langley Research Center,Hampton, VA.✝ Computational, Modeling & Simulation Branch, NASA LangleyResearch Center, Hampton, VA.⊕ Member, AIAACopyright 2002 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 a royalty-freelicense to exercise all rights under the copyright claimed herein forgovernment purposes. All other rights are reserved by the copyrightowner.

α angle of attack (degree)φ roll angle (degree)δ boundary layer height (in.)θc cone half angle (degree)

Subscriptsaw adiabatic wallB blunted nosetipb basee local value at boundary layer edgen model noseref Fay and Riddell stag. heating (Rn=0.125-in.)S sharp nosetipT transition onseto reservoir conditions2 stagnation conditions behind normal shock∞ free-stream conditionsw wall

IntroductionThermal effects resulting from boundary layer

transition during hypersonic ascent, cruise, or entry canrepresent an important thermal protection system (TPS)design constraint1. From a thermal protectionperspective, the success of the ceramic-based tilesutilized on the US shuttle orbiter was in some regardsthe consequence of a conservative (and costly) designphilosophy. Strategies for achieving an economicallyviable next generation space transportation system with

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an emphasis on risk reduction and enhanced crew safetymay include refined or alternative TPS concepts. Froman operations perspective, it has been suggested thatmetallic TPS may offer more durability at reduced cost.Relative to ceramic TPS however, the thermallimitations of current metallic systems imposetrajectory tailoring requirements in order to delaytransition to as low a Mach number as possible; this isto reduce the probability that turbulent heating levels donot exceed the peak levels experienced during thelaminar phase of entry2. With the shuttle orbiter,boundary layer transition concerns are primarilyassociated with re-entry. The designer of an extendedcruise hypersonic air breather faces additional transitionchallenges. Uncertainties in drag prediction3 andpropulsion system efficiencies4 (e.g. inlet mass capture,fuel mixing) resulting from the presence or absence ofboundary layer transition could impact vehicle andmission performance.

Until a credible mechanism based5 approach totransition prediction is developed, the TPS designer willcontinue to rely on prediction strategies that includeempirical methods derived from ground basedmeasurements. Wind tunnel based boundary layertransition criteria are usually considered conservative dueto influences of facility disturbances which presumablycause transition to occur at lower values of Reynoldsnumbers than may actually occur in flight5. Quiet windtunnel technologies developed at and incorporated intosupersonic and hypersonic wind tunnels at the NASALaRC in the 1980’s and 1990’s have clearly establishedthe influences of noise on transition and have advancedthe understanding of transition via stability experimentsconducted in these facilities6-27 as well as inconventional tunnels28-32. Despite advances in quietwind tunnel technology, relatively few low disturbancesupersonic or hypersonic facilities exist. Thoseoperational today are typically deficient in Reynoldsnumber relative to representative flight conditions andare generally not operated in a manner conducive for fastpaced aeroheating configuration assessment/screeningstudies. Thus, despite recognized limitations,conventional hypersonic facilities such as the NASALaRC 20-Inch Mach 6 Air Tunnel continue to serve asthe primary source for experimental data33-46 from whichto develop empirical methods for flight transitionprediction.

The purpose of this paper was to qualitativelyassess the acoustic disturbance environment of theNASA LaRC 20-Inch Mach 6 Air Tunnel; characterizefacility noise effects on parametric trends associatedwith hypersonic slender body transition; and aid in theinterpretation of transition criteria developed from dataobtained in a conventional hypersonic tunnel. Therelative disturbance environment of this conventionaltunnel was deduced via differences in smooth walltransition onset locations measured on two conicalmodels previously tested in the LaRC Mach 6 Nozzle

Test Chamber (NTC) Quiet Tunnel11-24. In addition,spectra associated with the tunnel freestreamfluctuations were made with an uncalibrated hotwire.While the disturbance growth within the boundary layerof the wind tunnel models was not measured at thistime (as in a stability experiment), the two sets ofexperiments are believed to represent the first directcomparison of transition onset between a conventionaland a low disturbance hypersonic wind tunnel operatedat both high and low noise environments usingcommon models at comparable freestream conditions.This direct comparison has important implications asthe effects of acoustic noise on transition onset are oftendetermined by operating the low disturbance facility in a“noisy” mode5-10, 17 (diverter valves normally open topromote a laminar nozzle wall boundary layer areclosed, resulting in a turbulent nozzle boundary layer).Although it has been suggested that this “noisy” modewould likely produce higher levels of acoustic radiationrelative to a conventional tunnel the potential effect hasnever been quantified (via comparative testing of modelsused in quiet tunnel research in a conventional facility).Also, as noted in Ref. 5, a supersonic low disturbanceenvironment has produced trends in transition onset(e.g. bluntness or angle of attack effects) that have beendifferent to that observed when the same facility is run“noisy”. This study presented an opportunity fromwhich to compare trends in slender body hypersonictransition under conventional tunnel conditions withthose found supersonically under high and low noiseconditions (measurements to identify parametric trendsat low and high disturbance levels were never attemptedin the Mach 6 NTC Quiet Tunnel).

In the present conventional hypersonic tunnelexperiment, two measurement techniques (separate windtunnel runs) were used to identify transition onset.Measurements of heat transfer rate and adiabatic walltemperatures were obtained independently on the conemodels at small angles of attack over a range of lengthReynolds numbers (0.8x106 to 16x106) that resulted inlaminar and turbulent flow. Wall-to-total temperatureratio for the laminar heating measurements and thelaminar adiabatic wall temperature measurements were0.59 and 0.86, respectively. Nosetip bluntness(0.0001< Rn <0.125-inch) and angle of attack (± 0, 0.5,1, 2, 4, 4.5 degree) effects on transition were obtainedto compliment experimental investigations on similarslender cones that were tested in conventionalhypersonic tunnels47-56, as well as cones tested in a lowdisturbance supersonic tunnel7-10. Correlation ofmeasured transition onset locations with linear stabilitytheory has been made. The evolution of the smoothwall surface heating from a laminar to a transitional andturbulent state are compared to those obtained withtransition forced via discrete surface roughness.

Characterization of the heating on complex shapesand quantifying the effects of surface roughness in termsof correlations derived from conventional ground based

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testing will continue into the near future. Most of theNASA’s recently proposed X-vehicles have been testedin the NASA LaRC 20-Inch Mach 6 Air Tunnel with amajority of the aerothermodynamic studies emphasizinghypersonic transition and the characterization of surfaceroughness effects33-46. While it is recognized thatimprovements in TPS technology have been made sincethe first flight of the US shuttle orbiter, most have notbeen flight demonstrated. A recent review of roughness-dominated transition suggests TPS technology forreentry vehicles in the near future may continue to beroughness dominated57. Traditional ceramic TPS tilessuch as those used on the Shuttle Orbiter often sufferlaunch-induced damage and/or develop protruding gapfillers. Both forms of local surface roughness have beenresponsible for the occurrence of early boundary layertransition in flight58. Stitching patterns found onthermal blankets produce another form of localroughness. Metallic TPS panels that were proposed foruse on the X-3333,59-60 could have been susceptible tothermally induced expansion/bowing producingroughness in the form of a wavy wall.

It is generally accepted that boundary layertransition can result from parametric instabilities, modeinteractions, or transition bypass mechanisms (a termcommonly used to identify transition modes whichbypass the linear growth process of disturbances).When vehicle surface roughness are present (a typicalbypass), it is believed that facility noise fromconventional tunnels has little effect on transition.Experimental studies have suggested that while noisemay have little effect for roughness heights largeenough to be considered effective61 (turbulence initiatedimmediately downstream of the roughness element site),there still may be an influence of wind tunnel noise ontransition onset data derived from roughness that are lessthan effective62-63. Based upon experimental evidencesuggesting the susceptibility of less than effectiveroughness elements to acoustic disturbances,quantification of the conventional facility disturbanceenvironment is essential.

Experimental MethodsModels

The present tests in the LaRC 20-Inch Mach 6 AirTunnel utilized two models that were originallyconstructed for testing in the LaRC Mach 6 NTC QuietTunnel. The original stability experiments were to beconducted on a 25-inch long (sharp tip) 5-degree straightcone model shown schematically in Fig. 1a.Undocumented surface temperature measurements madeon the 5-degree straight cone in the LaRC Mach 6 NTCQuiet Tunnel revealed that boundary layer transitiononset did not occur.

Consequently, the emphasis of the stability testsshifted to the second conical model (with a flared base).The purpose of the flare was to promote boundary layerinstability via an adverse pressure gradient to insure

transition would occur on the model within the limitedquiet flow Reynolds number capability of the Mach 6NTC Quiet Tunnel.

(a) 5 deg straight cone and nosetip

dimensions (inches)

(b) 5 deg flared cone (Model 93-10) and nosetipdimensions (inches)

Fig. 1. Schematic diagram of slender conemodels.

A schematic diagram of the flared cone modelgeometry is shown in Fig. 1b. Measuring 20-inches inlength (sharp tip) the model base diameter is 4.6-inch.The first 10-inch section of the model consists of a 5-degree half angle cone followed by a 10-inch sectioncomprised of an outward flare. Tangency was specifiedat the cone/flare junction. An arc radius of 93.07-inchesdefined the flare curvature. Details of the 5-degree halfangle flared cone model (designation 93-10) can befound in Ref. 16.

Both models were constructed thin walls fabricatedfrom 15-5 stainless steel to reduce surface heatconduction effects and to bring the models to thermalequilibrium as quickly as possible during a run. Theflared cone model was constructed with fiveinterchangeable nosetips (Rn= 0.0001, 0.03125,0.06250, 0.09375, and 0.125-inch) fabricated from 13-8stainless steel (see Fig. 1a-b) while the straight conehad three nosetips (Rn= 0.0001, 0.03125, 0.06250).The surface finish on both models was originally highlypolished to minimize waviness and roughness induced

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effects on boundary layer stability and, for the presenttest, appeared to be free of large surface scratches(despite several entries into the quiet tunnel and thesubsequent long-term storage).

Discrete and distributed surface roughness wereutilized to force boundary layer transition to compareagainst smooth body transition and to insure fullyturbulent flows were obtained in the present study.Photographs of the boundary layer trips are shown inthe inset of Fig. 2. Discrete roughness elements (ofdiamond planform shape) used in this study wereoriginally conceived to simulate a raised shuttle TPStile as described in Ref. 33. Individual roughnesselements (0.050 x 0.050-in.) were fabricated fromadhesively backed teflon tape of various thickness (k=0.0045, 0.0065, 0.0115-in.). The roughness elementwas applied to the model surface at various axiallocations (x/L= 0.1, 0.2, and 0.4) along the array ofthermocouples. In addition, discrete and distributed(randomly dispersed) surface roughness in the form ofprecision glass microspheres (d=0.0115-in.) wereapplied to the model surface near x/L= 0.1. The effectsof the different forms of roughness will be detailed in afuture report.

Fig. 2. 5 deg flared cone (Model 93-10)installed in the NASA LaRC 20-Inch Mach 6Tunnel (boundary layer trips- inset).Model Instrumentation

The original 5-degree straight cone wasinstrumented with a total of ninety-four type K(Chromel/Alumel) thermocouples that were tack weldedto the model thin wall backside along a single ray. Thethermocouples were spaced axially at 0.25-inchintervals. Access to the model interior was not possibleand verification of the thermocouple locations was madeby non-intrusive X-Ray measurements. The localmodel wall thickness was nominally 0.030-inch alongthe location of the streamwise row of thermocouplesand 0.060-inch elsewhere (actual local wall thickness ateach thermocouple junction was determined withultrasound measurements-see Data Reduction and

Uncertainty section). Forty-six 0.040-inch diameterstatic pressure orifices were located on the opposite sideof the model although pressure measurements were notattempted with this model during the present test series.

The cone flare model was constructed andinstrumentation locations determined in a similarfashion. A total of fifty-one type K thermocoupleswere tack welded to the model thin wall backside alonga single ray. The thermocouples were spaced axially at1-inch intervals between model stations x=2 and 9inches and 0.25-inch intervals from model stations x=9to 19.75-inches. The local model wall thickness wasnominally 0.030-inch along the location of thestreamwise row of thermocouples and 0.060-inchelsewhere. Twenty-nine 0.040-inch diameter staticpressure orifices were located on the opposite side of themodel.

Facility Descriptions

Although the Mach 6 NTC Quiet Tunnel hassince been disassembled, at the time of the originalquiet tunnel experiments, both facilities were locatedwithin the same lab and shared a common air supplyline and heater element. For a short period, both weremanaged under what is now known as theAerothermodynamic Laboratory Complex (ALC). Thiscomplex presently consists of four hypersonic windtunnels that represent much of the nation's conventionalaerothermodynamic test capability. Collectively, theyprovide a range of Mach number, unit Reynoldsnumber, and normal shock density ratio64. This rangeof hypersonic simulation parameters is due, in part, tothe use of two different test gases (air, andtetraflouromethane), thereby making the facilitiesunique national assets. The ALC facilities are relativelysmall and economical to operate, hence ideally suited forfast-paced aerodynamic performance and aeroheating, andtransition studies aimed at screening, assessing,optimizing, and bench-marking (when combined withcomputational fluid dynamics) advanced aerospacevehicle concepts and basic fundamental flow physicsresearch.

20-Inch Mach 6 Air Tunnel: Heated, dried,and filtered air is used as the test gas. Typical operatingconditions for the tunnel are: stagnation pressuresranging from 30 to 500 psia; stagnation temperaturesfrom 300 to 540 degree F; and freestream unit Reynoldsnumbers from 0.5 to 8 million per foot. A two-dimensional, contoured nozzle is used to providenominal freestream Mach numbers from 5.8 to 6.1.The test section is 20.5 by 20 inches; the nozzle throatis 0.399 by 20.5-inch. A bottom-mounted modelinjection system can insert models from a shelteredposition to the tunnel centerline in less than 0.5-sec.Run times of up to 15 minutes were achieved for theadiabatic wall temperature measurements. For thetransient heat transfer tests, the model residence time in

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the flow was limited to 20 seconds. A detaileddescription of this facility may be found in Ref. 64

In an attempt to attenuate noise from upstreampiping/air control valves, the settling chamber wasenlarged and recently retrofitted with a series ofacoustically damping porous screen elements. Thistechnology7 was based upon quiet tunnel experience atLaRC and was designed to reduce pressure fluctuationsin the settling chamber to approximately 0.005 % ofthe stagnation pressure.

Mass flow and total temperature fluctuationswere measured in this facility65 at reservoir conditions(Po = 125 psia and To = 410 degree F.) very close to thereservoir conditions associated with the quiet tunnel lowdisturbance condition (Po = 130 psia and To = 350 degreeF.). In that work, a dual wire constant temperatureanemometer was used to infer mass and totaltemperature fluctuations of 2.4% and 1.4%,respectively. Freestream spectra from this study at 125psia began to roll off at approximately 10 kHz withlittle measurable fluctuations above the electronic noisefloor out to the limits of the measurement near 160kHz. As discussed in Ref. 65, the mass fluctuationswere converted to pressure fluctuations and were quotedas 3.4%, which the authors claim was comparable tothe results of Ref. 66 which reported 2.8% using a pitotprobe. These quantitative measurements were madeprior to the addition of the acoustically damping porousscreen elements in the settling chamber and should berepeated.

Mach 6 Nozzle Test Chamber QuietTunnel: Heated and dried air was used as the test gas.Typical low disturbance operating conditions for thetunnel were: stagnation pressures ranging from 80 to130 psia, stagnation temperatures up to 350 degree F,and a maximum freestream unit Reynolds numbers of2.8 million per foot. A contoured axisymmetric slowexpansion nozzle was used to provide a nominalfreestream Mach number of approximately 5.9. Thenozzle exit diameter was 7.49 inches with the flowexhausting into an open jet test section; the nozzlethroat diameter was 1.0-inch. This facility had nomodel injection system thus transient based heat transfermeasurements could not be obtained. Run time for theadiabatic wall temperature measurements varied between30 and 60 minutes. Details concerning the facility, thesize of the quiet flow envelope and measurements of thedisturbance environment are discussed in Ref. 12.

Test Conditions and Setup

Reservoir and corresponding free stream flowconditions for the present tests in the LaRC 20-InchMach 6 Air Tunnel are presented in Table 1. The quiettunnel test condition is represented at Po = 130 psia andTo = 350 degree F. The freestream properties weredetermined from the measured reservoir pressure andtemperature and the measured pitot pressure at the testsection. The standard procedure used to compute flow

conditions for the ALC facilities uses the viscosityformulation given by Chapman-Cowling and is detailedin Ref. 67. However, for the present test the computedReynolds number was based upon the less accurateSutherland formulation for viscosity to maintainconsistency with the method employed to compute flowconditions for tests made in the LaRC Mach 6 NTCQuiet Tunnel. Computed Reynolds numbers basedupon Sutherland’s formulation are generally 5% lowerrelative to that inferred from Chapman-Cowling.

In the present test, the ratio of model base area totunnel cross sectional area for the cone flare model (93-10) was 0.042 and 0.036 for the straight cone. In bothwind tunnel experiments a base mounted cylindricalsting supported the conical models. A limited numberof runs were made with an uncalibrated hotwirepositioned in the freestream just outside the modelshock layer. The probe was attached to a holder thatwas mounted to the cylindrical sting. Model angle-of-attack (pitch) and sideslip (yaw) were referenced to thegeometric centerline of the tunnel and were set to zeroin the tunnel using a combination of accelerometerbased angular measurements and a laser alignmentsystem. It should be recognized that geometric pitchand yaw angles may not represent actual flow pitch andyaw angles if flow angularity is present. A photographof the sting supported cone flare model is shown in Fig.2. Details of the cone flare model installation in theNASA LaRC Mach 6 NTC Quiet Tunnel can be foundin Ref. 16.

Test Techniqu es

Adiabatic wall temperature: In the originalstability experiments conducted in the low disturbancetunnel, the individual thermocouple temperaturemeasurements were monitored with time and used todetermine when the model had obtained a state nearthermal equilibrium. The resulting temperaturedistribution was used to identify transition onset. Thetest procedure for the quiet tunnel measurementsinvolved preheating the model by exposing it tohypersonic conditions for 30 to 60 minutes to achievethermal equilibrium. For the adiabatic wall temperaturemeasurements in the conventional tunnel test, the testprocedure was designed to approximate as closely aspossible this technique. That is, the model was injectedinto the hypersonic stream and allowed to reach a statenear thermal equilibrium. Higher mass flow rates withthe present conventional tunnel tests limited total runtimes to approximately 12 to 15 minutes depending onthe desired Reynolds number. Temperature timehistories obtained during each run were monitored andindicated when thermal equilibrium was approached.Typical time rate of change of temperature near thermalequilibrium was on the order of 0.5 degree per minute.At the low Reynolds number laminar conditions (Re∞ < 1.1 x 106) this criteria could not be reached and requiredthat the model be preheated prior the start of the run.

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The model was not allowed to cool between runs inorder to minimize the time required to reach thermalequilibrium on subsequent runs.

Transient thin skin heat transfer: The thinwall construction of the conical models made it possibleto apply the transient thin skin calorimeterymeasurement technique to infer heat transferdistributions along the streamwise array ofthermocouples. The lack of a model injection systemand placement of the model inside the nozzle preventedthis type of heating technique to be exploited in the lowdisturbance tunnel. In the current conventional tunneltest, separate tunnel runs were required to obtaintransient heating data and adiabatic wall temperaturedata. For the transient technique, the hypersonic streamconditions were established with the model in asheltered position. The model was then injected intothe flow and thermocouple temperature time historieswere acquired. The model was allowed to cool betweenruns in order to obtain isothermal conditions necessaryfor the calculation of heat transfer.

Surface static pressure: Surface pressuremeasurements were obtained concurrent with theadiabatic wall temperature or heat transfer data and weremade with an electronically scanned pressure (ESP)transducer. The full-scale range of the absolutepressure transducer was 0.36 psia. The long run timesassociated with the adiabatic wall temperaturemeasurements provided more than adequate time forsettling. The relatively short test times associated withthe transient heating measurements did not provideenough settling time. Although not presented in thisreport, the flared cone surface pressure distributions wereutilized to determine if the model had any angle ofattack issues such as those associated with the previoustests in the low disturbance tunnel24.

Flow Visualization: Flow visualization in theform of schlieren was used to verify model incidenceangle and to complement the surface temperature andheating measurements. The LaRC 20-Inch Mach 6 AirTunnel is equipped with a pulsed white-light, Z-pattern,single-pass schlieren system with a field of viewencompassing the entire test core. The model length didnot permit an entire view of the cone flare length. Thelight source was pulsed for approximately a 3 msduration. Images were recorded on a high-resolutiondigital camera and will be enhanced with commercialsoftware for future analysis.

Data Reduction a nd Uncertainty

A 16-bit analog-to-digital facility acquisitionsystem was used to acquire data. The facility, modelthermocouple, and pressure data was collected by thissystem at a rate of 50 samples per second over a 20second interval during each run. The raw data weretransferred to a Hewlett-Packard 9000 computer for datareduction and storage.

Thermocouple mV output was referenced to anelectronic ice point and was converted to engineeringunits via a standard type K lookup table. Accuracy ofthe surface temperature measurement is estimated to bebetter than ±5 degrees F. Heating rates under transientconditions were calculated from backside surfacetemperature measurements as discussed in detail in Ref.68. The data were not corrected for surface conductionor curvature effects. The resulting heating distributionsare presented in the form of a normalized heatingcoefficient, h/href where href corresponds to thetheoretical stagnation point heating to a sphere usingthe method of Ref. 69. The reference radius is 0.125-inches which corresponded to the nosetip of largestbluntness. The conical models were originally designedto measure adiabatic wall temperatures and thus precisewall thickness measurements critical for inferringaccurate heating magnitudes were never obtained. Toimprove the accuracy associated with the heatingdistributions obtained from the present tests, ultrasoundmeasurements made at the vicinity of the thermocouplejunction were used to determine the local wallthickness. Deviations from the nominal 0.030-inchwall thickness specified in the model drawings werenoted and accounted for in the data reduction. For thetransient thin skin heating measurements, the overallexperimental uncertainty is estimated to be better than±15%. Conduction effects near the model base mayhave contributed to a larger uncertainty in this region.Repeatability of the cone flare normalized heat transferdistribution over several wind tunnel entries with twosharp nosetips was found to be generally better than±5% as shown in Fig. 3 and is representative of theentire test series. As the primary goal of the presenttest was the determination of transition onset, theaccuracy of the heating measurements were more thanadequate for indicating the departure from a referencelaminar boundary layer state.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 5 10 15 20 25

6811 029 02/01/01 #1 φ = 0 deg6811 025 02/01/01 #2 φ = 0 deg6825 003 09/27/01 #1 φ = 0 deg6825 156 10/18/01 #1 φ = 0 deg6825 017 10/01/01 #1 φ = 180 deg

h/h

ref

x, inches

Repeatability 5%

Uncertainty ± 15%(shown)

Test run date nosetip model orientation

Fig. 3. Repeatability of heating distributionin conventional Mach 6 Tunnel. 5 deg. flaredcone, M∞∞∞∞=6 (conventional), Re ∞∞∞∞=4.3 x 10 6/ft ,αααα =0 deg, Rn=0.0001-in.

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The ESP pressure measurement system wascalibrated prior to each run. The measured surfacepressure was expressed in nondimensional form, Ps/P∞,and in terms of a pressure coefficient. Measuredreservoir values of Po and To are estimated to beaccurate to within ±2 percent.

The accurate determination of angle of attack wasof utmost importance for the present slender cone testsas small model angles of attack relative to the flow canhave a large effect on the theoretically computedfrequency of the most unstable second-mode disturbance26. The angle of attack of the cone models was set tozero degrees by placing two calibrated accelerometerbased inclinometers along the 0 and 180 degree rays ofthe cone surface. A model incidence of zero degrees wasinferred when the absolute angular magnitude of bothinclinometers was equal. Uncertainties in model angle-of-attack associated with accelerometer basedmeasurements are estimated to be ±0.07 degree. Asshown in Fig. 3, rolling the model 180 degreesproduced no changes in the heating distribution andindicated that flow angularity was not an issue. Basedon schlieren images, the model incidence was observedto change by no more than 0.05 degree due to thermalgradients in the support hardware during the longduration runs. The sideslip angle of the cone modelswas set to zero degrees by alignment of a laser lightsheet along the longitudinal array of pressure orifices.Uncertainties in model sideslip angle associated withoptical based measurements are estimated to be ±0.2degree.

Computational MethodsPreface

Mean flow computations associated with the sharp noseconical models were performed with two Navier-Stokessolvers. LAURA, the benchmark code of theAerothermodynamics branch at NASA LaRC, was usedto provide straight cone surface heating predictions forcomparison with laminar and turbulent measurement.Predictions provided by CFL3D were used to obtainboundary layer profile inputs used in the subsequentboundary layer stability analysis on the flared cone.

Mean Flow Calculations - LAURA

Computations were performed using theLAURA70-71 code (version 4.9.2). The LAURA(Langley Aerothermodynamic Upwind RelaxationAlgorithm) code is a three-dimensional, finite-volumesolver which includes perfect-gas, equilibrium and non-equilibrium chemistry models, and can be used to solvethe inviscid, thin-layer Navier-Stokes, or full Navier-Stoke equations. For the current study, the thin-layerNavier-Stokes equations were solved. Laminarcomputations were performed to determine heating ratesfor comparison with the laminar wind tunnel data, andto obtain boundary layer edge-parameters for futurecorrelations. Turbulent computations were performedfor comparison with turbulent wind tunnel data using

the algebraic Baldwin-Lomax72 model withmodifications73 for compressible flow and either a zero-length or Dhawan-Narashima74 transition length model.The transition onset location for the computations wasdetermined from the wind tunnel data. Solutions werecomputed on an axisymmetric, single-block (101 x 65)point grid. Grid adaptation was performed to align thebow-shock with the grid and produced nominal wall cellReynolds numbers on the order of 10. Freestreamconditions for the LAURA wind tunnel computationswere set to the freestream operating conditions of thecurrent test, which are listed in Table 1. For the windtunnel computations, a uniform, ambient 80 degree Fmodel wall temperature boundary condition wasimposed.

Mean Flow Calculations - CFL3D

Mean flows around the cone used in the stabilitypredictions were computed using CFL3D75-76, whichsolves the compressible, three-dimensional, thin-layerNavier-Stokes equations with a finite-volumeformulation. The code is characteristic-based, whereupwind-biased spatial differencing is used for theinviscid terms. The flux-difference-splitting method ofRoe77 was used to obtain fluxes at the cell faces. Allviscous terms were centrally differenced. The codeprovides for a variety of techniques that were used toaccelerate convergence to steady state. In addition tolocal time-stepping, grid sequencing and multi-griddingwere used. Grid sequencing allows the user to establisha converged or partially converged solution on a coarsergrid before proceeding to a finer grid level.Multigridding is used to eliminate long-wavelengtherrors on the finer grids, and thereby improveconvergence.

Except where indicated, the calculations wereperformed using adiabatic wall conditions on the conesurface. Extrapolation was used as the downstream(outflow) boundary condition and the free streamconditions specified in Table 1 were specified upstreamof the cone and were used as the far-field condition. Theshock was always captured within the domain.

The calculations were performed using a single-block grid with 137 nodes in the streamwise directionand 257 nodes in the cross-stream direction. The flowwas forced to be axisymmetric by computing only asingle azimuthal cell with width of 1 degree and periodicboundary conditions. Seven nodes of the streamwisegrid are upstream of the nose of the cone; the eighthnode coincides with the sharp cone tip. Four levels ofmulti gridding were applied at the finest grid. At least50,000 iterations were used on the finest grid for eachcalculation. Additional iterations resulted in negligiblechanges to the computed flow.

At a unit Reynolds number of 6.2 x 106/ft (notshown), the results using the full grid were comparedwith the results using a grid consisting of every otherpoint in the streamwise and cross-stream directions. Apointwise comparison of the computed velocities

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indicated that less than 1% of the points had velocitiesthat differed by more than 2% between the full andreduced grid. Almost all of the differences that exceeded2% were confined to the most upstream points, wherethe flow is stable and would likely result in minimalinfluences on the stability calculations.

Because the flow upstream of the flare is that of asimple sharp cone, this portion of the flow was alsocomputed using a boundary-layer code. Results of thestability analysis using profiles from the boundary-layercode and from CFL3D were indistinguishable andindicated that the boundary layer was properly resolvedin the Navier-Stokes calculations. Stabilitycalculations for different grid resolutions in the wall-normal direction also indicated that the 137 x 257 gridgives grid-converged stability results. Unlike theprevious investigation by Balakumar and Malik26 usingan earlier version of CFL3D, a solution sensitivity tothe flux limiters and level of convergence was notobserved. In all cases, the default min-mod limiter wasused.Linear Stability Analysis

Stability analysis is performed using the LangleyStability and Transition Analysis Code (LASTRAC78.The LASTRAC code provides both quasi-parallel LinearStability Theory (LST) and Parabolized StabilityEquations (PSE) methods for stability analysis and N-factor correlation of boundary layers. The currentrelease of LASTRAC can handle 2-D, axisymmetric orinfinite swept-wing boundary layers. Three majorcomputational modes; quasi-parallel LST, linear PSE,and nonlinear PSE can be chosen. Effects ofstreamwise curvature due to the flare and transversecurvature associated with the axisymmetric geometry areincluded in the stability analysis. Transverse curvaturehas a stabilizing influence on the axisymmetric first andsecond modes and a destabilizing influence on theasymmetric first mode disturbances79. Streamwisecurvature is not important in the case of a flared conesince the dominant effect on the stability results isassociated with the strong adverse pressure gradient. Ata free-stream Mach number of 6, the boundary layeredge Mach number is approximately 5.4. Theoretically,the dominant instability mode on the flared cone isexpected to be second mode. The second-mode wave ismost unstable when it is two-dimensional oraxisymmetric. All second-mode calculations presentedhere were done for axisymmetric waves. Theasymmetric first-mode waves were computed by usingdifferent azimuthal wave numbers, n, defined as thenumber of waves along the azimuthal direction.

Results and DiscussionPreface

Discussion of the experimental results has beenorganized in the following manner. First, the resultsfrom the conventional hypersonic tunnel are presentedand focus on the effects of Reynolds number, wall

temperature ratio, nose bluntness, and angle of attack ontransition onset. Bluntness and angle of attack trendsare then compared to trends obtained from a supersonicquiet tunnel operated at low and high disturbance levels.The final section presents the direct comparison oftransition onset between a conventional and lowdisturbance hypersonic wind tunnel using a commontest model and transition detection method. Toconclude, correlations of the transition onset locationwith linear stability prediction are made.

Conventional Tunnel

Transition Characteristics

Historically, many experimental methods80-81

(surface and flowfield measurements) have been used todetermine the location of boundary layer transition onsetand the length of the transitional flow downstream thateventually leads to fully developed turbulent flow. Inthis study, surface heat transfer, a parameter of directinterest to designers of aerospace vehicles, was used todefine transition onset. Normalized heat transferdistributions for the sharp tip (Rn=0.0001-inch) straightcone model are presented in Fig. 4a-c, for unit Reynoldsnumbers (Re∞/ft) of 6.2 x 106, 4.3 x 106, and 1.1 x 106

respectively. For consistency, the onset of boundarylayer transition at any given Reynolds number has beeninterpreted as the departure from the laminar heatingdistribution. For comparative purposes, laminar andtwo turbulent predictions are shown in each figure.Turbulence in the computations was initiatedinstantaneously (zero transition length) from (1) thenose and (2) from the measured transitional peak. Forclarification purposes, distinct points on the measuredheating distribution curve at Re∞=6.2 x 106/ft in Fig. 4ahave been identified with transition onset and thetransitional peak.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 5 10 15 20 25

Turbulent prediction from transition peak

No trip (natural transition)

h/h

ref

x, inches

Transition peak

Transition onset Fullydeveloped turbulent

?

Turbulent prediction from nose

Laminar prediction

(a) Re∞=6.2 x 106/ft

The transition peak has been shown to coincidewith the point of maximum intermittency82 andturbulent burst frequency52. At “high” Reynolds

AIAA-2002-2743

9


number, the transition peak is clearly observed buttypically becomes more difficult to identify as transitiononset moves aft (e.g. lower Reynolds number orincreased nose bluntness). The transition peak is oftenidentified with the end of transition and hence theestablishment of fully developed turbulent flow.Inspection of Fig. 4a suggests that the point of fullydeveloped turbulent flow lies some distance downstreamof the measured transitional peak and is consistent withthe experimental observations of Refs. 52 and 82. Thisdistinction, however, between the transition peak andfully developed turbulent flow is of importance whenvalidating CFD turbulent heating prediction.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 5 10 15 20 25

laminar predictionturbulent prediction from transition peak

No trip (natural transition)0.0045-in. trip k/δ = 0.30.0065-in. trip k/δ = 0.40.0115-in. trip k/δ = 0.7

h/h

ref

x, inches

Trip

stat

ion

Turbulent predictionfrom nose

Laminar prediction

Single diamond trip

(b) Re∞=4.3 x 106/ft

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 5 10 15 20 25

laminar predictionturbulent prediction from noseNo trip (natural transition)0.0045-in. trip k/δ = 0.150.0065-in. trip k/δ = 0.220.0115-in. trip k/δ = 0.38

h/h

ref

x, inches

Tri

ps

tati

on

Turbulent predictionfrom nose

Laminar prediction

Single diamond trip

(c) Re∞=1.1 x 106/ft

Fig. 4. Comparison of measured smooth anddiscrete trip heating distributions withlaminar and turbulent prediction, 5 deg.straight cone, M∞∞∞∞=6 (conventional), αααα =0 deg,R n=0.0001-in.

In Fig. 4b, natural “smooth” body transition atRe∞=4.3 x 106/ft has been compared to transition forcedwith discrete boundary layer trips. The ratio of trip-to-boundary layer height (k/δ) varied from 0.3 to 0.7. Asexpected, the larger trip heights are more effective atbringing transition onset closer to the trip location(x=2-in). Typical of all forms of roughness tested inthe present study, agreement between the measuredsmooth wall and the forced turbulent heating withturbulent prediction was generally better than ±5%. InFig. 4c natural “smooth” body transition at Re∞=1.1 x106/ft was not observed. The largest trip had only amarginal effect. Laminar heating predictions weregenerally within 5% of measurement.

Wall Temperature Ratio and Reynolds Number Effects

The heating distributions in Fig. 4 were inferredfrom temperature-time measurements whereby themodel residence time in the flow was only a fewseconds. The model wall temperature under adiabaticconditions (separate run-residence time in flowapproximately 14 minutes) was, naturally, higher thanthat measured with the transient heating technique.Wall temperature can affect hypersonic transition. Inthe context of linear stability theory, hypersonicboundary layers on a slender cone near M∞ = 6 wouldhave both first and second mode disturbances. Wallcooling would be expected to stabilize first modedisturbances while destabilizing the second mode83-84.

0

100

200

300

400

0 5 10 15 20 25

Tw

, d

egF

x, inches

AdiabaticTw/To = 0.86

@ t = 14 minutes

TransientTw/To = 0.59

@ t = 1.5 seconds

Run 13_Re∞ = 1.1 x 106/ft

Run 265_Re∞ = 1.1 x 106/ft

Run 227_Re∞ = 7.8 x 106/ft

Run 17_Re∞ = 7.8 x 106/ft

Fig. 5. Comparison of model temperaturedistributions for recovery temperature(adiabatic wall) and transient heatingmeasurements, 5 deg. straight cone, M∞∞∞∞=6(conventional), Re ∞∞∞∞=1.1 and 7.8 x 10 6/ft ,αααα =0 deg, Rn=0.0001-in.

A correlating parameter often used is the wall-to-total temperature ratio, Tw/To. The manner in whichTw/To is varied can impact the transition process in aground based tunnel. Changing the stagnationtemperature to produce a variation in Tw/To would likely

AIAA-2002-2743

10


change the freestream disturbance environment85. In thepresent test series M∞, Re∞, and To were fixed and Tw

was dictated by the model residence time in the flow.The difference in straight cone temperature is shown inFig. 5, for the Reynolds number range in theconventional tunnel, Re∞=1.1 x 106/ft and Re∞=7.8 x106/ft. The backside wall temperature distribution alongthe cone obtained 1.5 seconds after model exposure atthe lowest Reynolds number was essentially constant(Tw=75 degree F; Tw/To=0.59). At the same Reynoldsnumber under adiabatic conditions the wall temperaturewas higher (280 degree F; Tw/To=0.86). Similar wall-to-total temperature ratios were obtained at Re∞=7.8 x106/ft with surface temperature increases (385 degree F;Tw/To=0.90) associated with boundary layer transitionnear adiabatic conditions.

Despite the wall-to-total temperature differencesin the present test on the sharp cone, the two methodsfor determining transition onset yielded equivalentlocations for Re∞< 3.2 x 106/ft as shown in Fig. 6a-d.

0

0.03

0.06

0.09

0.12

0.15

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

h/h

ref

T w/T

0

x, inches

Re∞ =1.1 x 106/ft

Re∞ = 1.1 x 10 6/ft

Adiabatic Tw /To = 0.86

Transient Tw/To = 0.59

(a) Re∞=1.1 x 106/ft, Po = 60psi, To = 425 deg F

0

0.03

0.06

0.09

0.12

0.15

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

h/h

ref

Tw

/T0

x, inches

Re∞ = 2.2 x 106/ft

Re∞ = 2.2 x 106/ft

Re∞ = 1.1 x 106/ft


Transient Tw /To = 0.59

(bas

ed o

n he

at t

rans

fer)

Tra

nsi

tio

n O

nse

t

(b) Re∞=2.2 x 106/ft, Po = 125psi, To = 450 deg F

0

0.03

0.06

0.09

0.12

0.15

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

h/h

ref

Tw

/T0

x, inches

Re∞ = 2.8 x 106/ft

Re∞ = 2.8 x 106/ft

Re∞ = 1.1 x 106/ft

Adiabatic Tw/To = 0.86


(bas

ed o

n he

at t

rans

fer)

Tra

nsi

tio

n O

nse

t

(c) Re∞=2.8 x 106/ft, Po = 130psi, To = 350 deg F

0

0.03

0.06

0.09

0.12

0.15

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

h/h

ref

T w/T

0

x, inches

Re∞ = 2.8 x 106/ft

Re∞ = 2.8 x 106/ft

Re∞ = 1.1 x 106/ft


Transient Tw/To = 0.59(b

ased

on

heat

tra

nsfe

r)

Tra

nsi

tio

n O

nse

t

(d) Re∞=2.8 x 106/ft, Po = 155psi, To = 450 deg F

The transition onset point from the transientheating distributions (lower half of figure) has beenindicated at a location where the nondimensionalizedheating departed from laminar reference level measuredat Re∞=1.1 x 106/ft. The method for estimatingtransition onset via the adiabatic wall temperaturedistribution (upper half of figure) was consistent withthat used for tests in the quiet tunnel and consisted ofdetermining the intersection of two straight linespassing through the laminar region and the temperaturerise near the transition peak as discussed in Ref. 16.While it is felt that the recovery temperature slopemethod is more subjective, the onset locationsdetermined in this manner agree relatively well to thoseinferred via surface heating. Above Re∞= 3.2 x 106/ft,Fig. 6e-h, small but consistent differences in the onsetlocation became apparent. At Re∞=6.2 x 106/ft, Fig.6h, transition onset inferred from the heatingdistributions (Tw/To=0.59) was approximately 0.5-in.

AIAA-2002-2743

11


downstream of that inferred from the adiabatic walltemperature distribution (Tw/To=0.86). This was not theanticipated trend whereby a decrease in Tw/To would beexpected to destabilize the second mode resulting in aforward movement in the location of transition onset.It should be also noted that in several investigationsconducted in conventional hypersonic facilities51 littlechange in transition onset Reynolds numbers for.59<Tw/To< 0.86 were reported. Further discussion isdeferred to the section devoted to correlation ofmeasurement to linear stability prediction.


0

0.03

0.06

0.09

0.12

0.15

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

h/h

ref

T w/T

0

x, inches

Re∞ = 3.2 x 106/ft

Re∞ = 3.2 x 106/ft

Re∞ = 1.1 x 106/ft


(bas

ed o

n he

at t

rans

fer)

Tra

nsi

tio

n O

nse

t

(e) Re∞=3.2 x 106/ft, Po = 180psi, To = 450 deg F

0

0.03

0.06

0.09

0.12

0.15

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

h/h

ref

Tw

/T0

x, inches

Re∞ = 4.3 x 106/ft

Re∞ = 4.3 x 106/ft

Re∞ = 1.1 x 106/ft



(bas

ed o

n he

at t

rans

fer)

Tra

nsi

tio

n O

nse

t

(f) Re∞=4.3 x 106/ft, Po = 250psi, To = 450 deg F

As expected, an increase in Reynolds number,Fig. 6a-h, moved the transition onset point on the conesurface upstream. The first indication of a transitionpeak (localized maximum in the nondimensionalizedheating distribution) occurred at Re∞ = 4.3 x 106/ft.

At Re∞= 2.8 x 106/ft, the nominal reservoirtemperature and pressure conditions corresponding to thequiet tunnel condition were 350 degree F and 130 psia,respectively. This relatively low temperature reservoir

condition had been selected to reduce hot-wire overheatrequirements for that test series. Concerns that thisquiet tunnel operating condition lie too close to the airliquefaction curve were assessed in the conventionaltunnel by testing at different reservoirpressure/temperature combinations so as to hold Re∞/ftconstant at Re∞= 2.8 x 106/ft. The largest difference intransition onset, Fig. 6c-d, was approximately 0.25-in.and was considered insigificant.

0

0.03

0.06

0.09

0.12

0.15

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

h/h

ref

T w/T

0

x, inches

Re∞ = 5.4 x 106/ft

Re∞ = 5.4 x 106/ft

Re∞ = 1.1 x 106/ft



(bas

ed o

n he

at t

rans

fer)

Tra

nsi

tio

n O

nse

t

(g) Re∞=5.4 x 106/ft, Po = 325psi, To = 475 deg F

0

0.03

0.06

0.09

0.12

0.15

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

T w/T

0

x, inches

Re∞ = 6.2 x 106/ft

Re∞ = 6.2 x 106/ft

Re∞ = 1.1 x 106/ft



(bas

ed o

n he

at t

rans

fer)

Tra

nsi

tio

n O

nse

t

h/h

ref

(h) Re∞=6.2 x 106/ft, Po = 365psi, To = 475 deg F

Fig. 6. Comparison of smooth bodytransition onset inferred from heatingdistributions with those determined via wal lrecovery temperature 5 deg. straight cone,M ∞∞∞∞=6 (conventional), αααα =0 deg, Rn=0.0001-in.

Bluntness Effects

While primarily intended to provide data forcomparison to the quiet tunnel results, the presentconventional tests also served to assess the effects ofnose bluntness and angle of attack on transition onset.

AIAA-2002-2743

12


The effect of nose bluntness at Re∞= 7.8 x 106/ft isshown in Fig. 7a-c. Consistent with Ref. 50, nosetipbluntness delayed boundary layer transition. Transitiononset for the sharp tip (Rn=0.0001-in.) occurred at x=5-inches with the transition zone extending at leastanother 10-in. downstream. An increase in the nosetipradius to 0.0625-inches extended the laminar boundarylayer to x=12.25-inches with the transition zoneextending perhaps to the end of the model.

0

0.03

0.06

0.09

0.12

0.15

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

x, inches

Re∞ = 7.8 x 106/ft

Re∞ = 1.1 x 106/ft



T w/T

0

h/h

ref

(bas

ed o

n he

at t

rans

fer)

Tra

nsi

tio

n O

nse

t

Re∞ = 7.8 x 106/ft

(a) Rn=0.0001-in.

0

0.03

0.06

0.09

0.12

0.15

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

x, inches

Re∞ = 7.8 x 106/ft

Re∞ = 7.8 x 106/ft

Re∞ = 1.1 x 106/ft



Tra

nsi

tio

n O

nse

t

(bas

ed o

n he

at t

rans

fer)

T w/T

0

h/h

ref

(b) Rn=0.03125-in.

The pronounced transition peak associated withthe sharp nosetip, Fig. 7a, was attenuated as nosebluntness increased. For vehicle design, and inparticular the hypersonic airbreather designed forsustained cruise, the observed heating overshootassociated with the transition peak may be of interest asthe majority of slender hypersonic vehicles successfullyflown have had some degree of bluntness (e.g. re-entryF). If thermal limitations associated with sharp leadingedges are overcome (e.g. heat pipe technology, advanced

ceramics) the so-called “transitional heating overshoot”could become more of a design factor in future TPSdesign.

At this Reynolds number, Re∞= 7.8 x 106/ft Fig.7a-c, the spatial disparity discussed in the previoussection between transition onset locations obtained atTw/To= 0.59 and 0.86 progressively increased toapproximately 1-in. as the straight cone nosetip wasblunted.

0

0.03

0.06

0.09

0.12

0.15

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

x, inches

Re ∞= 7.8 x 106/ft

Re ∞= 7.8 x 106/ft

Re∞ = 1.1 x 106/ft



Tra

nsi

tio

n O

nse

t(b

ased

on

heat

tra

nsfe

r)

T w/T

0

h/h

ref

c) Rn=0.0625-in.

Fig. 7. Nose bluntness effects on smoothbody transition onset inferred from heatingand recovery temperature 5 deg. straightcone, M∞∞∞∞=6 (conventional), αααα =0 deg, Re∞∞∞∞=7.8x 106/ft, Po = 475psi, To = 475 deg F

Angle of Attack Effects

The effects of angle of attack on straight conetransition onset location are presented Fig. 8a-b, forthree nosetip bluntnesses at Re∞=7.8 x 106/ft andRe∞=4.3 x 106/ft, respectively. For comparativepurposes, the corresponding Reynolds number basedupon freestream conditions and nose radius (ReR,n) wasalso tabulated. The windward and leeward transitiononset location has been normalized to the locationmeasured on the sharp cone at α = 0 degree.Comparisons of the present data to other publisheddata47-49 obtained at similar test conditions withapproximately the same model geometry are shown,Fig. 8a. The general trends appear consistent with theseconventional tunnels. Specifically, for a sharp cone, anincrease in angle of attack moved transitioncontinuously rearward on the windward ray and forwardon the leeward ray with no evidence of a reversal intransition onset location. Comparison of the data setsindicate that the laminar running length along the sharpcone windward ray in the LaRC conventional tunnel(relative to the corresponding sharp cone transitionlocation at α = 0 deg) was greater than that inferred byStetson and Krogmann (Refs. 47-49). As small

AIAA-2002-2743

13


differences in θc and ReR,n exist between the data sets itis difficult to quantify the differences in magnitude.

The variation of the normalized transitionlocation on the windward ray with angle of attack forthe blunted cone exhibited a different trend than thesharp cone and are consistent with Stetson (Ref. 49).

0

1

2

3

4

5

1 0.5 0 -0.5 -1

0.000 65 7.8 x 106

0.014 20,300 7.8 x 106

0.029 40,625 7.8 x 106

0.000 450 9.7 x 106 θc = 5 deg (Krogmann)

0.000 800 9.7 x 106 θc = 8 deg (Stetson)

0.020 64,650 19.4 x 106 θc = 8 deg (Stetson)

XT

/(X T

S) αααα

= 0

deg

αααα/θθθθcWindward Ray Leeward Ray

Rn/Rb ReR,n Re∞∞∞∞ ft-1

(a) Re∞=7.8 x 106/ft, Krogmann M∞=5. (Ref.47);Stetson M∞=5.9 (Ref.49)

At the time, Stetson postulated that the effects ofbluntness diminished with increasing angle of attack,thus the location of transition onset for the bluntnosetips would eventually cease to move rearward atsome small incidence angle. In the present test, thelocation of transition onset for the bluntest nosetip (Rn

= 0.125-in and ReR,n = 40,625), Fig. 8a, initially movedrearward for α /θc < 0.2 (hence the increased laminarrunning length with increasing incidence).

0

1

2

3

4

5

1 0.5 0 -0.5 -1

0.000 35 4.3 x 106

0.014 11,200 4.3 x 106

0.029 22,400 4.3 x 106

XT

/(X T

S) αααα

= 0

deg

αααα/θθθθcLeeward RayWindward Ray


(b) Re∞=4.3 x 106/ftFig. 8. Nose bluntness and angle of attackeffects on windward/leeward-ray smooth bodytransition locations. Normalized to sharpcone values, 5 deg. straight cone, M∞∞∞∞=6(conventional)

In contrast to the sharp cone trend wheretransition continues to move rearward, the transitiononset location for this bluntest nosetip reversed andbegan to move forward as incidence angle was furtherincreased (α /θc > 0.2). At that time, Stetsonconjectured that the blunt cone angle of attack trends(curves) would turn and eventually approach the sharpcone levels. The behavior postulated by Stetson wasexhibited by the present data, Fig. 8b, for Re∞=4.3 x106/ft. Stetson’s bluntness parameter was Rn/Rb and didnot account for Reynolds number effects.

0

1

2

3

4

5

1 0.5 0 -0.5 -1

0.000 35 4.3 x 106

0.000 65 7.8 x 106

0.014 11,200 4.3 x 106

0.014 20,300 7.8 x 106

0.029 22,400 4.3 x 106

0.029 40,625 7.8 x 106

XT

/(X

TB

) αααα=

0 d

eg

αααα/θθθθcLeeward RayWindward Ray


Fig. 9. Nose bluntness and angle of attackeffects on windward/leeward-ray smooth bodytransition locations. Normalized to bluntcone values, 5 deg. straight cone, M∞∞∞∞=6(conventional)

In Fig. 9, the windward and leeward transitiononset locations presented in Fig. 8a-b have been re-normalized to the location measured on thecorresponding blunt nosetip at α = 0 degree.Expression of angle of attack trends in windwardtransition onset location in terms of the nose bluntnessReynolds number (ReR,n) suggest that angle of attackeffects (α /θc < 1) on transition onset appear to bemitigated for ReR,n> 20,000.

Conventional Hypersonic and Low DisturbanceSupersonic Comparisons

The effects of tunnel noise on high-speed laminar–turbulent transition are well documented and Schneider5

presents an excellent review. When comparinghypersonic parametric trends inferred frommeasurements on a slender cone to those obtained atsupersonic conditions, one must keep in mind thatdifferent instability mechanisms are most likely present.At supersonic conditions first mode instabilities prevail,while at the hypersonic conditions of the present tests,

AIAA-2002-2743

14


both first and second mode instabilities are likelypresent.

Bluntness Effects

The effects of nose bluntness on slender conetransition in the presence and absence of a lowdisturbance freestream environment at supersonicconditions are presented in Fig. 10 (taken from Ref.10).

106

107

1 10 102 103 104 105 106

Re T

ReR,n

M∞ = 3.5 Re∞ = 8-12 x 106 /ft cone

(Chen)

M∞ = 3.5 Re∞ = 3-9 x 106 /ft cone

(Chen)

M∞ = 6 Re∞ = 7.8 x 106

/ft(present results-coneand flared cone)

conventional noisy

low disturbance

noisy

Fig. 10. Comparison of present nosebluntness effects on smooth body transitionto supersonic trends (Ref.10) obtained in theNASA LaRC M=3.5 Quiet Tunnel at low andhigh disturbance levels. αααα =0 deg

The supersonic (M∞ = 3.5) transition onsetlocation was inferred from surface pitot pressuremeasurements made on a 5 degree half angle cone at α =0 degree near adiabatic conditions. Chen’s datapresented in Fig. 10 were obtained in tabular form andlimited to unit Reynolds numbers close to that obtainedin the present test. The transition onset Reynoldsnumber based on freestream conditions (ReT) has beencorrelated against nose bluntness Reynolds number(ReR,n) for both a low disturbance environment and at“noisy” conditions facilitated by closing the quiet tunnelboundary layer bleed slots. Chen and Schneider pointout that under noisy conditions, small increases in nosebluntness did not delay transition in contrast to thatinferred from tests under quiet conditions. The presentM∞=6 data were obtained in a conventional hypersonictunnel at Re∞=7.8 x 106/ft. This unit Reynolds numberwas selected so as to insure transition on the flared coneoccurred upstream of the flare adverse pressure gradient(x = 10-in.) and transition onset measurements made onboth the straight cone and the flared cone could bepresented. Third-order polynomial fits to the data havebeen applied to clarify trends. Although the magnitude

of ReT at hypersonic conditions was different, it is clearthat the conventional tunnel exhibits the sameparametric trends as the supersonic data at lowdisturbance conditions (pronounced increase in ReT withincreasing nose bluntness Reynolds number). Thissuggests that perhaps the test section wall radiated noisefrom the quiet tunnel operating “noisy” is severeenough to mask the bluntness effect. In this specialcase, the parametric trend from the hypersonicconventional tunnel (at perhaps more moderatedisturbance levels) appears to be qualitatively moreconsistent with that inferred from the supersonic tunneloperated at low disturbance conditions. At supersoniclow disturbance conditions it appeared that bluntnesseffects initially became apparent for ReR,n between10,000 and 20,000. Without additional measurements itis difficult to quantify the ReR,n threshold at M∞ = 6where bluntness effects prevail.

Angle of Attack Effects

The effects of angle of attack on slender conetransition in the presence and absence of a lowdisturbance freestream environment at supersonicconditions are presented in Fig. 11 taken from Ref. 9.

0

1

2

3

4

5

-1-0.500.51

XT/(

XT

S) αααα=

0 d

eg

αααα////θθθθ C

Windward Ray Leeward Ray

M∞ = 6 Rern = 65 Re∞ = 7.8 x 106 /ft

(present results-cone and flared cone)

M∞ = 3.5 Rern = 95-1,400

Re∞ = 1.14-16.8 x 106 /ft cone

(King)

noisy

low

conventional noisy

disturbance

Fig. 11. Comparison of present angle o fattack effects to supersonicwindward/leeward-ray smooth body transitionlocations (Ref. 9) obtained in the N A S ALaRC M=3.5 Quiet Tunnel at low and highdisturbance levels. Normalized to sharp conevalues

The supersonic (M∞ = 3.5) transition onsetlocation was inferred from surface pitot pressuremeasurements made on a 5 degree half angle cone at α =0 degree near adiabatic conditions. The transition onsetReynolds number based on freestream conditions (ReT)has been plotted against normalized angle of attack(α /θc) for both a low disturbance environment and at“noisy” conditions facilitated by closing of the quiet

AIAA-2002-2743

15


tunnel boundary layer bleed slots. King observed thatunder supersonic low disturbance conditions, increasesin angle of attack above α /θc > 0.12 did not produce arearward movement of windward transition onset as wasinferred from measurements under “noisy” conditions.The present M∞=6 conventional hypersonic tunnel datawere obtained at Re∞=7.8 x 106/ft and did not exhibitthis behavior. As in Fig. 10, this unit Reynoldsnumber was selected so as to ensure transition on theflared cone occurred upstream of the flare adversepressure gradient (x = 10-in.) and transition onsetmeasurements made on both the straight cone and theflared cone could be presented. For these tests conductedat supersonic and hypersonic conditions, ReR,n< 1,500.Curve fits to the data have been applied to clarify trends.It is clear that the conventional tunnel exhibited thesame parametric trend as the supersonic data at “noisy”conditions. In this special case, the parametric trendfrom the conventional tunnel appears to be opposite tothat inferred from the supersonic low disturbance tunnel.The trends displayed in the supersonic low disturbancefacility remain inconclusive as the aft end of the conewas outside the region established as “quiet”.

Comparison of Hypersonic Transition Onset in aConventional and a Low Disturbance Facility

A direct comparison of conventional vs. lowdisturbance tunnel transition onset locations at adiabaticwall conditions for the straight and flared cone atcomparable freestream conditions is shown, Fig. 12a-b,for Re∞=2.8 x 106/ft. To the author’s knowledge thisrepresents the first comparison of transition onsetlocation between a conventional and low disturbancehypersonic tunnel utilizing common models andtransition detection techniques.

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

20-in Mach 6(conventional )

Tw

/To

x, inches

Re

T = 2

.91

x 10

6

* R

e T >

5.8

5 x

106

5 deg cone

* Transition not observed on model (XT based on model length of 25-in.)

(a) 5 deg cone.

The conventional tunnel straight cone transitiononset location (Fig. 12a) inferred from the walltemperature distribution near adiabatic conditions was

located x = 12.5-in. at a corresponding transitionReynolds number (ReT) of 2.91 x 106/ft. The methodfor estimating transition onset via the adiabatic walltemperature distribution was consistent with that usedfor tests in the quiet tunnel and consisted of determiningthe intersection of two straight lines passing throughthe laminar region and the sharp temperature rise nearthe transition peak (see Fig. 6d) as discussed in Ref. 16.At the corresponding unit Reynolds number in theMach 6 Nozzle Test Chamber Quiet Tunnel, theboundary layer on this same model remained completelylaminar16. Thus, based upon the 25-in. model lengthReT > 5.85 x 106. The transition onset Reynoldsnumber under low disturbance conditions is a factor of 2or more relative to that measured on a straight cone inthe LaRC conventional hypersonic tunnel. This iscomparable to the factor of 2.3 measured on a straightcone by Ref. 9 at supersonic “quiet” and “noisy”conditions. Unfortunately, the hypersonic lowdisturbance tunnel was not operated “noisy” for thelimited tests conducted with the straight cone model anda direct comparison to a conventional tunnelmeasurement cannot be made.

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

Mach 6 NTC low disturbanceMach 6 NTC noisy

20-in Mach 6 (conventional )

T w/T

o

x, inches

Re T

= 2

.89

x 10

6

Re T

= 3

.84

x 10

6

5 deg cone flare

Re T =

2.3

4 x

106

(b) 5 deg flared cone

Fig. 12. Comparison of present smooth bodytransition onset locations to that obtained i nthe NASA LaRC M=6 NTC Quiet Tunnel atlow and high disturbance levels. M ∞∞∞∞=6,Re ∞∞∞∞ =2.8 x 106/ft, αααα =0 deg, Rn=0.0001-in.

Because transition on the straight cone was notobserved in tests conducted in the Mach 6 Nozzle TestChamber Quiet Tunnel, emphasis of the stability testswas placed on the flared cone. The flare was designed toproduce a nearly constant boundary layer thickness thatwas expected to enhance the likelihood of transition via

AIAA-2002-2743

16


the second mode rather than the first mode. Since themost unstable second mode frequency is determined bythe boundary layer thickness, the integrated N factor forthe second mode becomes larger than that associatedwith the first mode. The geometry modification wassuccessful and transition onset from second modeinstability on the flared cone model in the lowdisturbance tunnel run “quiet” occurred at x = 16.25-in(ReT = 3.84 x 106)16 as indicated in Fig. 12b. Theinfluence of acoustic disturbances on flare conehypersonic transition was conservatively estimated byrunning the quiet tunnel in a “noisy” mode (divertervalves normally open to promote a laminar nozzle wallboundary layer are closed resulting in a turbulent nozzleboundary layer). As expected, transition onset movedforward to x = 10-in. (ReT = 2.34 x 106).

In the “noisy” mode of the hypersonic lowdisturbance tunnel, transition onset occurred earlier thanthat measured in the conventional hypersonic tunnel,Fig. 12b, which suggests higher levels of freestreamacoustic radiation relative to a conventional tunnel. Theconventional tunnel flared cone transition onset locationinferred from the wall temperature distribution nearadiabatic conditions was located at x = 12.25-in. with acorresponding transition Reynolds number (ReT) of 2.89x 106. The transition onset Reynolds number under lowdisturbance conditions is a factor of 1.3 greater to thatmeasured on flared cone in the LaRC conventionalhypersonic tunnel and a factor of 1.6 relative to theflared cone run in the quiet tunnel run “noisy”. It isnoteworthy that transition onset between the straightcone and the flared cone occurred within a distance of0.25-inch of each other and suggests that the initialboundary layer instability and growth primarily occurredin the zero pressure gradient region on the flared cone (x< 10-in.).

106

107

107 108

5 deg cone M=6 LaRC conventional (present results)5 deg cone M=7.9 LaRC conventional (Stainback)5 deg cone M=7.3 AMES conventional (Mateer)

Re

T

Re∞∞∞∞/m

(a) Cones at hypersonic conditions as reported in(Refs. 53, 54)

Comparison of hypersonic unit Reynoldsnumber effects on 5 degree sharp cone transition onset

(taken from Refs. 53 and 54) with the present straightcone data are shown in Fig. 13a. The present data andthat from Stainback are similar in magnitude andexhibit the, so-called, unit Reynolds number effectwhereby radiated noise intensity from the tunnel wallboundary layer varies with Reynolds number anddominates the smooth body transition process. Moreoften than not, unit Reynolds number effects arepresented log/log and the trends are characterized with astraight line fit (see Fig13b). The discrete data in Fig.13a however, indicates the complexity of the transitionprocess and the influence of wall radiated noise from thetest section walls. Near Re∞/m = 1 x 107 the LaRCresults from Stainback and the present study plateaubefore resuming the nearly linear increase in ReT withRe∞/m. The Ames transition onset data from Mateerwere obtained with Helium gas injection in the nozzleboundary layer which presumably affected the levels ofthe test section wall radiated noise. Their measurementsindicate a much smaller variation in transition Reynoldsnumber with increasing unit Reynolds number.

106

107

107 108

Flat plate M=3.5 LaRC low disturbance5 deg cone M=3.5 LaRC low disturbanceFlat plate M=3.0 AEDC Tunnel D (12' x 12')Flat plate M=3.7 JPL 20"Flat plate M=3.7 AEDC Tunnel A (40" x 40")Flat plate M=6 LaRC conventional (20" x 20') - unpub.5 deg cone M=6 LaRC conventional (20" x 20")5 deg flared cone M=6 LaRC conventional (20" x 20")5 deg flared cone M=6 LaRC NTC low disturbance

Re T

Re∞∞∞∞/m

LST prediction for N = 10

Presentresults}

(b) Cones and flat plates at supersonic conditionsas reported in (Ref.8)

Fig. 13. Comparison of transition onsetReynolds numbers with present data.

Reynolds number based on transition onset forcones and flat plates at supersonic conditions (takenfrom Ref. 8) with the present hypersonic straight coneand flared cone data are plotted against unit Reynoldsnumber (per meter) in Fig. 13b. The AEDC resultshave been corrected to the onset of transition asindicated by Ref. 8. Also included is unpublished flatplate transition onset data also obtained in theconventional LaRC 20-Inch Mach 6 Air Tunnel. Thepresent Mach 6 flared cone and flat plate data obtained ina conventional hypersonic tunnel exhibit the classicunit Reynolds number effect as discussed on the straight

AIAA-2002-2743

17


cone in Fig. 13a. For Re∞/m > 9 x 106 the straightcone and flared cone transition onset Reynolds numbersare very consistent despite the lower thermocouplespatial resolution on the flared cone model (andincreased uncertainties in transition onset location)Above this value of ReT, transition onset has occurredon the cone section of the flared cone and transitiononset locations between the two models should beidentical. As expected, below Re∞/m = 9 x 106 adisparity between the transition onset Reynolds numberfor the two conical models developed due to theinfluence of the flare. At the lowest unit Reynoldsnumber, the straight cone boundary layer was whollylaminar while the flare adverse pressure gradient haspresumably destabilized the boundary layer andpromoted transition on the model.

Linear stability theory at supersonic conditionssuggest that transition should occur on cones at lengthReynolds numbers that are lower than on flat plates.Measurements made in a low disturbance environment(namely the LaRC supersonic quiet tunnel8-not shown)are consistent with this prediction and have shown cone-to flat plate transition Reynolds number ratios less thanunity-in the range of 0.8 to 0.9. In contrast,experimental data obtained in conventional tunnels havehistorically shown the opposite trend. Specifically,measurements at supersonic Mach numbers inconventional tunnels80 have indicated cone-to flat platetransition Reynolds number ratios greater than unity-inthe range of 2.2 to 2.5 (and 1.6 to 1.9 for M∞ = 6). Assuggested by Beckwith (Ref. 7) the observation thatReT,cone / ReT,plate < 1 (for conventional tunnels) may bedue to the faster boundary layer growth on a flat platerelative to a cone and thus, stronger receptivity of theflat plate to the incident acoustic field from theturbulent test section walls found in the conventionaltunnels.

Consistent with historical observations, thepresent data from the Mach 6 conventional tunnel(Re∞/m < 1 x 107) indicate that the straight cone andflared cone transition onset Reynolds numbers werehigher than the corresponding flat plate data (see Fig.13b) and hence would yield cone-to flat plate transitionReynolds number ratios greater than one. However, forRe∞/m > 1 x 107 the present data show that the straightcone and flared cone transition onset Reynolds numberwas actually lower than or nearly equal to that measuredon the flat plate (see Fig. 13b) and hence would yieldcone-to flat plate transition Reynolds number ratios lessthan one. Ironically, this observation at higherReynolds numbers at hypersonic edge Mach numbers, issomewhat consistent with those made in the supersoniclow disturbance tunnel. As noted in Ref. 5, the LaRCsupersonic low disturbance tunnel run “noisy” alsoyielded cone-to flat plate transition Reynolds numberratios less than one (opposite to what was expected viaPate’s80 cone-to-flat plate transition findings) and wasnever fully explained.

In general, the flat plate transition onsetReynolds numbers from the conventional LaRC Mach 6tunnel are consistently higher than the flat plate M=3and 3.7 data from the AEDC and JPL facilities. Sinceit has been shown that the disturbance field soundintensity correlates with test section size80 one mightexpect better agreement of the present smooth flat plateReT data to the JPL results. Despite the similar testsection dimensions to the JPL tunnel, other factors suchas Mach number effects on radiated tunnel wall noise,boundary layer receptivity on the flat plate, or the noisereduction technology in the conventional tunnel settlingchamber may all have contributed to the higher ReT

values measured on the flat plate in the conventionalLaRC 20-Inch Mach 6 Air Tunnel.

106

107

108

0 2 4 6 8 10 12 14

Blunt flight dataRe-entry F flight dataSherman flight dataRemainder of flight dataDiCrista ground-test collection

Re T

Me

Q

Q

N

N

Q

SC, FC

Est (ReT based on end on cone)

LaRC M∞ = 3.5LaRC M∞ = 6

CFC

FC

SC

SC

SC

QNCSCFC

Quiet tunnel run "quiet"Quiet tunnel run "noisy"Conventional tunnelStraight ConeFlared Cone

_

_

Fig. 14. Comparison of transition onsetReynolds number on sharp cones near zeroangle of attack in flight and ground test asreported in (Ref. 86) with present data.

Figure. 14 (adapted from Fig. 1 of Ref. 86)shows both flight and ground based transition Reynoldsnumbers for a range of edge Mach number (see Ref. 86for citations of these datasets). Variations of this figureare often used to indicate the inability of conventionalground facilities to properly simulate free flightconditions due to the higher disturbance levels generatedfrom radiated noise from wind tunnel walls. It alsoshows an increase in transition onset Reynolds numberwith increasing Mach number suggested by flight andground based measurements. The figure has beenmodified to include the present straight cone and flaredcone results obtained at Me = 5.4. Transition onsetReynolds numbers from the LaRC conventionalhypersonic tunnel are generally consistent with theground measurements reported by DiCrista (see Ref. 86)for sharp cones near α = 0 degree and the flight resultsof Sherman (see Ref. 86).

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Disturbance Environment and Correlation to LinearStabilty Prediction

While the present conventional tunnelexperimental data set has permitted direct comparison oftransition onset to that measured in a hypersonic lowdisturbance tunnel, the lack of a one-to-onecorrespondence in terms of a stability experiment stillexists. Characterization of the freestream disturbanceenvironment and identification of dominate frequenciesand associated growth rates are critical for any stabilityexperiment conducted in a ground based facility.Exploratory tests to examine hot-wire survivability inthe conventional LaRC 20-Inch Mach 6 Air Tunnelwere conducted to determine the feasibility of obtainingfuture freestream and boundary layer spectra with acalibrated wire.

Preliminary free stream noise measurements weremade with an uncalibrated hot-wire operated by aconstant temperature anemometer. The addition of atwo stage particulate filter appeared to have alleviatedsome of the concern with particulates (wire breakage)described in early hotwire measurements attempted inthis facility65. Data (not shown) at reservoir pressuresfrom 15 to 130 psi indicated that the free streamspectrum begins to roll off at approximately 10 kHz.At 15 and 30 psi the voltage spectra appear smoothwith the exception of spikes clearly attributable toelectronic noise. At reservoir conditions correspondingto conditions run in the low disturbance tunnel (Po =130 psi, To = 350 degree F) the spectrum containsspikes between 50 and 100 kHz, but it is impossiblewithout more data to determine if they are flow or hot-wire related. At approximately 125 kHz the spectrumfalls to the level of the instrument noise floor which isa factor of 250 below the spectral amplitude at 10 kHz.Qualitatively, it appeared that there were no detectabledisturbances above the electronic noise level of thecurrent instrumentation at the dominant second modefrequencies (see next section).

Mean flow and stability calculations were done atseveral unit Reynolds numbers listed in Table 1. Inaddition, the effects of wall temperature were examinedby assuming a wall temperature of 80.3 degree F (300K) to approximate the model surface temperatureassociated with the transient heating measurements.For all cases, the N factor, which represents howinstability waves grow, was computed for a range ofunstable disturbance frequencies. The predicted first-mode N factors as a function of the streamwise distancex for a unit Reynolds number of 2.89 x 106 /ft areshown in Fig. 15. The first-mode calculations weredone at adiabatic wall conditions for a disturbancefrequency ranging from 40 to 100 kHz and an azimuthalwave number from n = 3 to n = 30. The mostamplified azimuthal wave number was found to bearound 20 for most cases. The first-mode N factor atthe measured transition onset location was

approximately N = 2. The results shown in Fig. 15were computed by integrating N factors for eachindividual asymmetric first mode wave. Alternatively,one can compute N factors by maximizing the growthrate (and thus, switch modes) at each downstreamlocation. The latter method results in a larger N factor.Transition correlations for low speed infinite sweptwing boundary layers indicate that tracking individualmodes preserves more flow physics and yields better Nfactor correlation.

0 5 10 15 200

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

70kHz, n = 21

Range of frequencies = 40-100kHz n = 3-30

x, inches

N

N = 2

N = 3

Conventionaltunnel transition

Quite tunnel transition

Fig. 15. Flared cone first-mode N factors o fvarious disturbance frequencies and azimuthalwave numbers M ∞∞∞∞=6, Re ∞∞∞∞=2.8 x 1 0 6/ft, αααα=0deg, Rn=0.0001-in., adiabatic wall condition

The corresponding second mode quasi-parallelLST N-factors of various disturbance frequencies(ranging from 20 to 340 kHz) are shown in Fig. 16a-bfor cold wall and adiabatic wall conditions, respectively.The most unstable frequency under adiabatic conditionswas predicted at 230kHz and is consistent with earlierflare cone stability predictions made by Balakumar26.The N-factor value at the measured transition onsetlocation for this frequency was about 3.8 for the presentinvestigation as compared to a value of about 7.8 underlow disturbance conditions. The presence of both firstand second mode disturbances on the conical modelstested in the conventional tunnel is likely but cannot beverified at the present time as hot-wire measurements inthe boundary layer were not attempted.

Several possible reasons have been suggested toexplain the disparity in N-factor between the lowdisturbance and conventional wind tunnel environment.The differences in measured transition onset could beattributed to different transition mechanisms in the twoexperiments (e.g. first mode vs. second mode), as the N

AIAA-2002-2743

19


factor for the most unstable first mode frequency wasnot much smaller than that predicted for the secondmode (2 versus 3.8) but such an explanation is purelyconjecture. A small N-factor at transition onset mayalso suggest that early nonlinear interaction could bepresent in the conventional wind tunnel due to a higherdisturbance environment. An earlier investigation87

using nonlinear PSE indicated that nonlinear effectswere important for the Mach 8 sharp cone experimentconducted by Ref. 88. For the present experiment,nonlinear interactions involving both second-mode andasymmetric first-mode disturbances may contribute totransition. It is also possible that transition in theconventional tunnel may be the result of nonlinearmode interactions28 and interpretation of the resultsbased on linear stability theory may not be adequate.Further studies, both experimental and computational,are necessary to clarify these issues.

N

0 5 10 15 200

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

240kHz

Range of frequencies = 20 - 340kHz

x, inches

N = 4.5


(a) Cold wall, Tw = 80.3 deg F (300K)

Instabilities associated with hypersonic boundarylayers are quite sensitive to wall thermal conditions83.Stability calculations have indicated that wall-coolingdestabilizes second-mode disturbances while stabilizingthe first mode. Fig. 16a shows predicted flared conesecond mode N factors obtained for a “cold” wall with atemperature of 80.3 degree F (300 K). As anticipated,the most amplified instability wave frequency increasedto 240 kHz for the cold wall case because the boundarylayer has thinned. This frequency is close to the earlierstability predictions by Balakumar26 which indicated aslightly larger shift (up to 260kHz). Compared to theadiabatic wall case, the N factors increased byapproximately 1.5 for the most amplified waves.Assuming the correlated N factor associated with secondmode transition remained at 3.8, the predicted change in

the transition onset location under cold wall conditionswould be at most a 0.5-in. shift towards the nose.Experimentally, observations made on the sharp straightcone (see Fig. 6c) and on the sharp flared cone (notshown) indicated that the transition onset locations wereindistinguishable for the adiabatic and transient cold-wall cases at Re∞ = 2.8 x 106/ft. As the thermocouplespatial resolution was 0.25-in. the experimental resultswere not conclusive. The lack of movement in thetransition onset location for adiabatic and cold wallconditions may also suggest that the linearamplification process is not as important in aconventional tunnel environment.

0 5 10 15 200

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Quiet tunneltransition


x, inches

N

N = 7.8

N = 3.8

230kHz

Range of frequencies = 20 - 340kHz

(b) Adiabatic wall condition

Fig.16. Flared cone second mode transitionN-factor values for present Mach 6 transitiononset location relative to that obtained i nthe NASA LaRC M=6 NTC Quiet Tunnel ata low disturbance level, M ∞∞∞∞=6, Re ∞∞∞∞=2.8 x10 6/ft, αααα =0 deg, Rn=0.0001-in.

Table 2 summarizes the N values at transitiononset for selected wind tunnel conditions. The tablealso includes second mode N factor values from linearPSE calculations. The PSE N factors are in generalgreater than the quasi-parallel LST N values, which areused more often in transition correlations. Greater Nvalues in the linear PSE calculations may be attributedto non-parallel effects and the upstream shift of theneutrally stable location when PSE is employed.Similar effects have also been observed in earlierinvestigations87,89 for hypersonic flat-plate and coneboundary layers. The N factors at transition onset forthe present experimental measurements fall in a range ofabout 3 to 4.5 using linear stability theory and about 4to 6.5 using linear PSE theory.

AIAA-2002-2743

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Concluding RemarksDespite advances in supersonic/hypersonic quiet

wind tunnel technology, relatively few low disturbancefacilities exist. Those in existence today are typicallydeficient in Reynolds number relative to representativeflight conditions, and are generally not operated in amanner conducive for fast-paced aeroheatingassessment/screening studies. Thus, conventionalhypersonic wind tunnels continue to serve as theprimary source for experimental data from which todevelop empirical methods for flight transitionprediction.

The purpose of this paper was to qualitativelyassess the acoustic disturbance environment of theNASA LaRC 20-Inch Mach 6 Air Tunnel andcharacterize facility noise effects on parametric trendsassociated with hypersonic slender body transition andto aid in the proper interpretation of transition criteriadeveloped from data obtained in a conventionalhypersonic tunnel. The relative disturbanceenvironment of this conventional tunnel was expressedvia differences in smooth wall transition onset locationsmeasured on two conical models previously tested in theLaRC Mach 6 Nozzle Test Chamber (NTC) QuietTunnel. Together, the two sets of experiments arebelieved to represent the first direct comparison oftransition onset between a conventional and lowdisturbance hypersonic wind tunnel using a commontest model and transition detection method. The resultsof this study suggest that a low disturbance tunneloperated “noisy” is likely to produce higher levels ofacoustic radiation relative to a conventional tunnel. Incontrast to trends at supersonic conditions, bluntnesseffects on hypersonic transition were not attenuated byfacility noise. At comparable freestream conditions, thetransition onset Reynolds number under low disturbanceconditions was a factor of 1.3 greater to that measuredon flared cone in the LaRC conventional hypersonictunnel and a factor of 1.6 relative to the flared cone inthe low disturbance tunnel run “noisy”. Navier-Stokesmean flow computations and linear stability analysiswere conducted to assess the experimental results andhave indicated N factors associated with transition onsetto be a approximately a factor of 2 lower than thatinferred from the corresponding low disturbance tunnelmeasurements. The lack of movement in the transitiononset location for adiabatic and cold wall conditionsmay suggest that the linear amplification process is notas important in a conventional tunnel environment.

AcknowledgmentsWithout the assistance of the following

individuals this work would not have been possible:Steve Wilkinson, Charlie Greenhalgh, Ed Covington,Pete Veneris, Ron Deans, and Kevin Meidinger formodel design information, surface inspection support,and model refurbishment; John Ellis, Grace Gleason,Rowland Hatten, and Steve Jones for wind tunnel

support; Sheila Wright and Mike Difulvio for dataacquisition assistance; Steve Wilkinson, SteveSchneider, Rudy King, Feng-J. Chen, and NdaonaChokani for analysis/computational support; CathyMcGinley for hot-wire measurements; and RichardWheless for documentation assistance. The authorsgratefully acknowledge their contributions and behind-the- scenes work.

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TABLE 1. Flow Conditions for the NASA LaRC20-Inch Mach 6 Air Wind Tunnel.

Re ∞∞∞∞ /ft (x106) M∞∞∞∞ Po(psia) To(°F)1.1 5.9 63 4212.2 5.9 124 4502.8 5.9 131 3522.8 5.9 156 4453.2 6.0 182 4444.3 6.0 257 4455.4 6.0 326 4726.2 6.0 372 4707.8 6.0 476 475

Shaded conditions represent a match to Mach 6NTC Quiet Tunnel reservoir conditions

TABLE 2. N-factor values correlated withmeasured transition onset on the flared cone.

Re ∞∞∞∞ /ft (x106) x T (in.) N (LST) N (PSE)2.2 14 3.0 4.02.8 12.25 3.8 6.4

2.8 (cold wall) 12.25 4.5 6.34.3 7.5 3.5 5.96.2 6.0 4.0 6.5

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