Flow characterization and boundary layer transition

Flow characterization and boundary layer transition

studies in VKI hypersonic facilities

Guillaume Grossir∗, Davide Masutti†, and Olivier Chazot‡

von Karman Institute for Fluid Dynamics, Chaussee de Waterloo 72, 1640 Rhode-St-Genese, Belgium

A summary of the activities performed over the last years at the von Karman Insti-tute for Fluid Dynamics in the frame of hypersonic boundary layer transition studies ispresented. Free-stream noise levels have been determined in the H3 Mach 6 conventionalwind tunnel using double hot-wires and modal analysis. In the Longshot wind tunnel atMach 10, an improved free-stream characterization method, based on the use of free-streamstatic pressure probes, has been applied, alleviating the needs for the limiting adiabatic andisentropic nozzle flow assumptions. Based on these improved flow characterization, naturaltransition experiments have been performed in both wind tunnels on 7 ◦ half-angle conicalgeometries at 0 ◦ angle of attack and with different nosetip radii. Measurements techniquesinclude either infrared thermography or flush-mounted fast response thermocouples in or-der to determine the transition onset location. Boundary layer instabilities are visualizedusing a LIF-based Schlieren technique at Mach 10, revealing rope-shape structures typicalof the second mode disturbances. Wall measurements using fast-response pressure sensorscomplete the investigations. Dominant boundary layer disturbances at various locationsalong the cone are determined and compared with theoretical predictions. The correspond-ing N-factor is inferred for each wind tunnel. A comparison of the different measurementtechniques is finally reported.

Nomenclature

Symbolsc Specific heat, J/(kg.K)

cNormalizing parameter (Pate’s correla-tion),

CFII Nozzle wall skin friction coefficientD Probe diameter, mm

k Thermal conductivity, W/(m.K)

L Probe length, mmm Mass flow, kg/s

M Mach numberN Maximum amplification factorp Pressure, Pa

Pr Prandtl numberr Recovery factorRB Base radius, mmRN Nosetip radius, mm

RaArithmetic average for surface rough-ness, µm

Re Reynolds numberReunit Unit Reynolds number, 1 /m

sDistance from a theoretically sharpnose, measured along the surface, mm

sB Transition onset location, mmsE End of the transition region, mm

St Stanton numberT Temperature, Ku Flow velocity, m/sx Distance along the cone axis, mm

y Distance along a normal to the surface,mm

Greekδ Boundary layer thickness, mmρ Density, kg/m3

Θ Entropy modeσ Sound-wave modeσ Standard deviationω Vorticity mode

∗PhD candidate, Aeronautics and Aerospace Dept., AIAA Student Member, [email protected]†Senior Research Engineer, Aeronautics and Aerospace Dept., [email protected]‡Associate Professor and Head of Aeronautics and Aerospace Dept., AIAA Member, [email protected]

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American Institute of Aeronautics and Astronautics

Subscriptse At the edge of the boundary layerr Recovery

t Stagnation condition

unit Based on a 1 m lengthw At the wall′ Fluctuating component

1 Upstream a shock wave

2 Downstream a shock wave∞ Based on a free-stream value

AbbreviationsLIF Laser Induced FluorescenceLST Linear Stability Theory

RMS Root Mean Square

VESTAVKI Extensible Stability and TransitionAnalysis

VKI Von Karman Institute

I. Introduction

The von Karman Institute for Fluid Dynamics (VKI) near Brussels, Belgium, houses more than 50 op-erational facilities dedicated to the study of various fluid flows. Among the Aeronautics and Aerospace

department, two wind tunnels are routinely used for the study of low-enthalpy hypersonic flows: the H3Mach 6 blowdown facility and the Longshot Mach 10 gun tunnel.

This paper first considers the H3 Mach 6 wind tunnel before focusing on results gathered in the Longshotwind tunnel. For each wind tunnel, the recent efforts which have been dedicated over the last 5 years to theflow characterization are reminded. In particular, the quantification of the free-stream noise levels is reportedfor the H3 wind tunnel using stagnation pressure and double hot-wire probes. Beside, in the Longshot windtunnel, direct measurements of free-stream quantities have been sought in order to reduce uncertainties onderived flow quantities such as the free-stream Mach and Reynolds numbers.

Based on the knowledge gathered and the improvements achieved, boundary layer transition studieshave then been carried out on various geometries. The present review focuses only on natural transitionexperiments along conical geometries whereas additional results obtained recently for both natural androughness induced transition on flat plates, cones and the Expert vehicle can be found in Refs. 1–5.

II. Motivation

Boundary layer transition is a critical phenomenon at hypersonic Mach numbers for several reasons. Theincrease of wall heat fluxes (up to an order of magnitude larger) is probably the most critical consequence6,7

and this has driven a large number of studies aiming at predicting the transition location in such high-speedflows. Recent reviews have underlined the complexity of the phenomenon,8,9 influenced by numerous param-eters and still associated to large uncertainties in the current predictions. This has lead to the conservativedesign of thermal protecting systems for reentry vehicles which is therefore detrimental to their payloads.

Hypersonic flight experiments are scarce because they are expensive, difficult to plan and execute suc-cessfully.10 Therefore, hypersonic wind tunnels are often used to duplicate, at least partially, these flightconditions. Nonetheless, the most accurate measurements achieved on wind tunnel models can be depreci-ated by poor knowledge of free-stream flow properties, which introduces bias, uncertainties, or both on thenon-dimensional quantities determined.

The accurate determination of free-stream flow properties is therefore a prerequisite to any boundary layertransition study. It is usually a challenging task for hypersonic wind tunnel operators because probes areintrusive and stagnation conditions may be influenced by high-temperature and dense gas effects. Difficultiesare often stressed further by the short test time available and limited instrumentation capabilities.

In addition, the boundary layer transition phenomenon is strongly influenced by the free-stream turbu-lence,11,12 which is dominated in hypersonic wind tunnels by acoustic radiations from the turbulent boundarylayers along the nozzle walls.13,14 Because this is not a scalar quantity (amplitude, direction and spectrumshould be considered), it is however difficult to characterize it precisely.

The objectives of the work performed at the VKI are therefore twofold. At first, efforts are dedicated tothe wind tunnels by improving the determination of their free-stream quantities and characterizing their free-stream turbulence levels when possible. This is used to increase the quality of experimental data collectedin these wind tunnels. In particular, the second objective is to improve the knowledge of the transitionphenomenon at hypersonic Mach numbers and to isolate the effect of compressibility on the stability ofhigh-speed boundary layers.

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III. Experiments in the H3 Mach 6 wind tunnel

III.A. H3 hypersonic wind tunnel

The boundary layer transition experiments at Mach 6 have been performed in the H3 hypersonic wind tunnelof the von Karman Institute for Fluid Dynamics. The VKI H3 test facility is a blow-down to vacuum typewind tunnel (figure 1).

Figure 1: Sketch of the VKI H3 hypersonic blowdown tunnel

This wind tunnel provides a uniform axisymmetric jet with a diameter of 12 cm at Mach 6. Dry air issupplied at stagnation pressures ranging from 6 to 35 bars. The test gas is heated up to a total temperatureof 500 K in order to avoid condensation in the test section. The free-stream unit Reynolds number typicallyvaries within 6–30 ·106 /m. The wind tunnel includes a model injection mechanism in order to avoid blockageand excessive heating of the model during start-up. The test chamber is vacuumed prior to each test usinga supersonic ejector. The test model is then injected once the Mach 6 free-jet is established. Further detailsabout this facility have been reported in Refs. 4, 15,16.

III.B. Flow characterization in the H3 wind tunnel

The hypersonic nozzle flow of the H3 wind tunnel has been recently characterized using both an array ofstagnation pressure probes and double hot-wires. The uniformity of the jet has been determined as well asthe free-stream disturbance levels.

Flow uniformity The free-stream Mach number uniformity has been inferred from an array of stagnationpressure probes, using the ratio of test section to reservoir stagnation pressures.17 Measurements have beenperformed at different axial locations. The uniformity of the hypersonic free jet along vertical and horizontalplanes are illustrated for one operating condition (Reunit,∞ = 18 · 106 /m) in figures 2a and 2b, respectively.

The nozzle of the VKI H3 has been designed with the method of characteristics for Mach 6. Its exitdiameter is about 154 mm. Measurements show that the jet core has a slightly higher Mach number withrespect to the nozzle design with a free-stream Mach number about 6.1.

The analysis of the maps in figure 2 reveals that the Mach number decreases at the sides of the jet core asvisible from 80 mm downstream the nozzle exit. This decreasing Mach number pattern is identified as a signof an overexpanded hypersonic jet. Blow-down facilities are often very sensitive to the back pressure imposedby the diffuser, a pressure slightly off the design can result in an overexpanded jet which can interfere witha slender wind tunnel model. These measurements are in agreement with the few profiles reported earlier inRefs. 15,18.

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(a) in the vertical plane (b) in the horizontal plane

Figure 2: VKI H3 free-stream Mach number uniformity (operating condition: Reunit,∞ = 18 · 106 /m)

In addition to this mean flow characterization, disturbance measurements have been performed in theVKI H3 wind tunnel with a double hot-wire and a high frequency response stagnation pressure probe alongthe nozzle axis.

Figure 3: Comparison of test section stagnation pres-sure fluctuations with results from BAM6QT (Ref. 26)

Test section stagnation pressure measure-ments Stagnation pressure measurements havebeen carried out in the test section by means of aKulite pressure transducer flush mounted in a Pitottube located along the centerline of the nozzle. Thestreamwise distance between the tip of the probeand the nozzle exit is about 10 mm. Another stag-nation pressure probe, connected to a reference pres-sure transducer outside of the test section, is locatedat a spanwise distance of 12 mm with respect to thecenterline. This latter probe is used to compensatethe temperature effect on the Kulite transducer asdescribed in Ref. 4.

In figure 3 the normalized RMS of the testsection stagnation pressure fluctuations is plottedagainst the free-stream unit Reynolds number. Nor-malized RMS values in the VKI H3 wind tunnelrange between 1.6–1.9. They exhibit a decreas-ing trend for free-stream unit Reynolds number in-crease, which is in line with observations reportedearlier in Ref. 29.

Values are compared to stagnation pressure fluctuations measurements which were reported recentlyfor the BAM6QT26 at a very similar free-stream Mach number. Stagnation pressure fluctuations in thefree-stream of the VKI H3 are slightly lower than the corresponding values from the BAM6QT when op-erated under noisy flow conditions. Benefits of the quiet flow capabilities of the BAM6QT wind tunnelare evident from this figure where pressure fluctuations drop by about two orders of magnitude, down toapproximately 0.015%.

Ref. 4 reports on the spectrum of the free-stream disturbances using the stagnation pressure probe. Arelatively flat spectrum is observed up to 30 kHz before a rapid decay. This decay closely corresponds tothe cut-off frequency of the sensor. Further efforts should be pursued to determine the spectrum of thefree-stream disturbances over a wider frequency range.

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Double hot-wire anemometer measurements Throughout the following analysis of hot-wire mea-surements, flow fluctuations in the potential core of the hypersonic jet have been assumed to be uniform.Although this hypothesis has not been proven yet for the VKI H3 wind tunnel, similar results can be foundin the literature, for example in Ref. 19 for a hypersonic Mach 5 jet. A combined analysis, described indetails in Ref. 4, allows to separate the different measurable fluid quantities.

In this analysis, only the results obtained by means of the calibration law suggested in Ref. 20 arereported. Statistical analysis are carried out for the mass flow and total temperature signals in orderto provide information about the intensity of the fluctuations of these two quantities. In figure 4, thenormalized RMS of the mass flow and total temperature fluctuations measured with the double hot-wireprobe are respectively plotted. This is given for different operating conditions of the wind tunnel as afunction of the free-stream unit Reynolds number.

(a) normalized RMS value for the mass flow (b) normalized RMS value for the total temperature

Figure 4: Free-stream fluctuations as a function of the free-stream unit Reynolds number (including com-parisons with data from Refs. 21–23 obtained in similar wind tunnels)

Normalized mass flow RMS fluctuations range between 3% and 7%, whereas normalized total temperatureRMS fluctuations are on the order of 1%. None of these quantities exhibit a clear trend as a function of thefree-stream unit Reynolds number.

Figure 5: Application of Kovasznay modal analysis31

to VKI H3 measurements: fluctuations of entropy, vor-ticity and acoustic modes

The latter results are similar to the ones reportedin Ref. 22 which were obtained in the Langley 20”Mach 6 wind tunnel and in Ref. 24 for the NASAAmes 3.5-foot and the NASA Langley Mach 8 vari-able density hypersonic facilities. Their results re-ported total temperature fluctuations on the orderof half the mass flow fluctuations and it was con-cluded that part of the total temperature fluctua-tions were related to the entropy spottiness due tothe absence of upstream thermal equalizer systems.Figure 4 indicates that total temperature fluctua-tions in the VKI H3 wind tunnel are about 20% ofthe mass flow fluctuations. It is also hypothesizedthat part of the high total temperature fluctuationsare caused by entropy spottiness.

Modal analysis The combined data reductionprocess detailed in Refs. 4, 32 allows to extract en-tropy, vorticity and acoustic fluctuations out of thedouble hot-wire and stagnation pressure measure-ments.

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Corresponding results are shown in figure 5. Entropy fluctuations range between 0.3% and 0.8%. Theirscatter is closely related to the fluctuations of the mass flow (figure 4a). Vorticity fluctuations are relativelystable around 0.6% for various free-stream unit Reynolds numbers.

The sound-wave mode (about 0.7%) is slowly decaying with the free-stream unit Reynolds number. Itappears to be predominant in the VKI H3 wind tunnel for almost the whole Reynolds number range, whereasthe entropy and vorticity mode fluctuations are both around 0.6%. The three modes are contributing togenerate disturbances in the free-stream flow and the sound-wave appears to be the one contributing themost. Ref. 11 demonstrated that such acoustic fluctuations play a dominant role in boundary layer transition.

III.C. Mach 6 conical model

Boundary layer transition experiments have been performed on a 7 ◦ half-cone. This model is assembledin two parts, one half made in stainless steel and the other half made in black Plexiglasr. This particularassembly allows for simultaneous measurements with high frequency pressure transducers (PCB 132A31)and an infrared thermocamera. An exploded view of the conical model is given in figure 6a.

(a) Exploded view (b) Sharp nose (magnification)

Figure 6: 7 ◦ half-cone wind tunnel model

This model has a total length of 265 mm and can be equipped with two exchangeable nosetips: a relativelysharp one (RN = 0.126 mm) and a slightly blunt one (RN = 2.5 mm). A magnified picture of the sharpnosetip is given in figure 6b.

A sketch of the stainless-steel side of the cone with the allowed sensor locations is given in figure 7. Theblack Plexiglasr is a very good insulator material and has been widely used at the VKI for quantitativeinfrared measurements. Plexiglasr thermal properties are summarized in Table 1. In order to achieve highand controlled emissivity at the surface, the model is painted with a special matte black paint. In such away, the emissivity of the surface can be considered close to a value of 1.

Figure 7: 7 ◦ half-angle cone (side view) and lo-cation of instrumentation

Table 1: Plexiglasr properties

ρ, kg/m3 c, J/(kg ·K) k, W/(m ·K)

1190 1464.4 0.19

III.D. Natural transition measurements at Mach 6

Surface pressure measurements in combination with infrared imaging have been performed in the VKI H3 hy-personic wind tunnel at different Reynolds number with a wall temperature to total temperature ratio Tw/Tt1

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equal to 0.59. The model was set to 0 ◦ angle of attack.

Comparison of different measurement techniques A typical Stanton number distribution alongthe conical surface is given in figure 8, where the large increase of the wall heat transfer coefficient arounds = 220 mm is due to the transition of the boundary layer from a laminar state to a turbulent one.

Figure 8: Stanton number distribution over a 7 ◦ half-angle cone in the VKI H3 wind tunnel at Reunit,∞ =18 · 106 /m

Different techniques are used to characterize the natural boundary layer transition process over the 7 ◦

half-cone in VKI H3 conditions. The transition onset location determined from infrared measurementsis plotted in figure 9 with a modified Stanton number (using a stagnation temperature Tt1 instead of arecovery temperature Tr), and compared to the RMS value of the pressure fluctuations normalized bythe computed Taylor-Maccoll mean wall pressure. The modified Stanton number has been normalized bythe cubic root of the Reynolds number in order to partially remove the influence of different free-streamconditions. Experimental results as a function of the Reynolds number are compared with Eckert’s theoryfor laminar and fully turbulent boundary layers.

Figure 9: Comparison of different measurement techniques: infrared (top) and amplitude of normalized wallpressure fluctuations (bottom). Prediction of the end of the transition region with Pate’s correlation givenby vertical dashed lines.

Experimental results depict boundary layer transition for unit Reynolds numbers of Reunit,∞ = 27.1 ·106 /m, 22.8 · 106 /m and 18 · 106 /m with an inferred natural transition location respectively at 133 mm,

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150 mm and 184 mm. For the lower Reynolds numbers cases at Reunit,∞ = 14.1 · 106 /m and 10.2 · 106 /m,the cone is too short to observe transition.

The evaluation of Pate’s transition correlation11 for cones (shown in figure 9) generally falls in themiddle of the transition region for a selected free-stream unit Reynolds number. The peak of surface pressurefluctuations occurs approximately in the middle of the transition region defined from infrared measurements.

Figure 10: Spectrum of boundary layer disturbances andcomparison with PSE (solid lines) and LST (dashed lines)computations (Reunit,∞ = 18 · 106 /m)

Comparison with Linear Stability The-ory The linear stability theory can be usedto predict the frequency and the growth rate ofthe most unstable perturbations in the bound-ary layer. Ref. 33 has shown that the highfrequency second mode instabilities were themost unstable waves over a sharp cone at hy-personic Mach number, which supported theexperimental results reported in Ref. 34.

Similar linear stability computations havebeen performed in the present investigation forcomparison with experimental results from theVKI H3 wind tunnel. The simulations havebeen performed using both the VKI in-houseVESTA Linear Stability code35 (LST) withperfect gas assumption and the LASTRAC 3DParabolized Stability Equations (PSE) code(NASA36).

Figure 10 shows a comparison betweenN -factors computed by means of LST andPSE codes and experimentally retrieved powerspectral densities for one experimental case(Reunit,∞ = 18 · 106 /m).

Figure 11: Streamwise evolution of amplificationN -factor computations (Reunit,∞ = 18 · 106 /m)

A satisfactory agreement between the theoretical andthe experimental dominant instabilities is observed. Nev-ertheless, a consistent shift in frequency is present in fig-ure 10 where the theoretical peaks have slightly higherfrequencies than the experimental results. Because thesame frequency shifts are shown for both LST and PSEcalculations, the effect of non parallel flow can be ex-cluded from the origin of such a discrepancy. However,both LST and PSE because of their basic assumptions donot include the so called secondary effects. Small imper-fections on the wind tunnel model surface, the real noisyenvironment of the wind tunnel, small misalignment orlocal variations of wall temperature on the model can beall considered secondary effects.

In figure 11 the amplification factors computed byPSE (solid red curves) and LST (dashed blue curves)codes are related to the experimental transition loca-tion (dashed vertical line) observed for a free-stream unitReynolds number of Reunit,∞ = 18 · 106 /m.

Analyzing figure 11 the value of the N -factor fromPSE computation is equal to 5.5, while from LST calculation the N -factor is slightly lower and equal to 4.8.This is in line with previous results reported in other conventional hypersonic wind tunnels37–39 suggestingthat a N -factor value of 5.5 provides a good approximation for the transition location in these noisy windtunnels.

Results for other free-stream conditions are detailed in Ref. 4 and yield approximately the same N -factorsfor such a conical geometry.

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IV. Experiments in the Longshot wind tunnel at Mach 10

IV.A. Longshot wind tunnel

Boundary layer transition experiments also have been performed in the Longshot hypersonic wind tunnelat the VKI. This facility is based on the principle of a gun tunnel with a piston used to compress the testgas with maximum stagnation pressures and temperatures respectively on the order of 2 500 × 105 Pa and2 200 K for the experiments considered here. A sketch of the wind tunnel is given in figure 12 and Ref. 40has recently described its mode of operation in more details.

Figure 12: Sketch of the VKI Longshot hypersonic gun tunnel

The Longshot wind tunnel allows for experiments at high Mach numbers within an environment quitefree of high-enthalpy effects (nitrogen is used here with maximum total enthalpies on the order of 2 MJ/kg)and at large Reynolds numbers in order to duplicate typical earth reentry trajectories.

This wind tunnel relies on a constant volume of compressed gas, hence stagnation conditions are decayingduring the typical 20 ms test time. This actually allows to scan a range of free-stream Reynolds numberduring a single experiment and contributes to increase its productivity. Typical flow conditions used fortransition studies were reported in Ref. 40 and range between Mach 9.5–12 while unit Reynolds numbers areon the order of 3.5–12 · 106 /m.

IV.B. Flow characterization in the Longshot wind tunnel

Recent efforts in this wind tunnel focused on reducing uncertainties on free-stream flow quantities. To thisend, slender static pressure probes have been designed and used to estimate the free-stream static pressure.Viscous interaction effects were accounted for based on numerical results, yielding a wall to free-streampressure ratio on the order of pw/p∞ = 0.96 (weak viscous interactions). One of the probes is illustratedin figure 13 and is equipped with a single Kulite pressure sensor XCQ-093-5psi at L

D = 24. The sensor ismounted within a cavity which is connected to the surface by four holes (inlet diameter: 0.6 mm) equallyspaced around the probe at 90 ◦ each. The detailed design and calibration procedure are reported in Ref. 41.

415.35mm

�6.6mm sensor at LD

= 24

Figure 13: Free-stream static pressure probe used for flow characterization

Free-stream static pressure measurements are used (in combination to the pressure and heat flux mea-surements at the stagnation point of an hemispherical probe with a diameter of 25.4 mm) to determine allfree-stream flow properties of interest. The procedure has been detailed in Ref. 41 and is based on the useof the Fay-Riddell equation.42 The interest of this method with respect to the one used previously43 is thatit only requires test section measurements to characterize the hypersonic flow. None of the questionableadiabatic and isentropic nozzle flow assumptions are required by this method.

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time, ms

Fre

es

tream

sta

tic

pre

ssu

re,P

a

0 5 10 15 200

200

400

600

800

1000

measured

theoretical

Figure 14: Comparison of free-stream static pressuremeasured and determined assuming an isentropic flowexpansion (time decay is inherent to the working prin-ciple of the Longshot wind tunnel).

These measurements revealed free-stream staticpressures about twice larger than expected from thetheoretical rebuilding method43 relying on an isen-tropic expansion assumption (figure 14). Good con-fidence has been obtained while using these staticpressure probes showing that difference is neitherattributable to viscous effects, nor sensor defect, norprobing geometry effects, nor probe misalignment.41

Other free-stream flow properties such asthe static temperature, local Mach number andReynolds number are consequently also influ-enced. Free-stream Mach number drops between 9.5and 12 depending on the test conditions considered,hence significantly lower than anticipated from theMach 14 nozzle design.41 In addition, independentresults such as flow visualization have confirmedthese measurements. This points out the deficien-cies of traditional rebuilding methods to detect non-isentropic expansions.

The contoured nozzle was designed using themethod of characteristics44 assuming an equilibriumflow and taking into account dense gas phenomenapresent in the reservoir (using an equation of state described in Refs. 45,46). The inviscid contour obtainedwas then corrected for the boundary layer displacement thickness based upon the correlation of Edenfield.47

Yet, the reasons for such nozzle flow behavior are not fully understood and still subject to investigations.The possibility of flow condensation in the free-stream while operating standard conditions was ruled out bydedicated experiments reported in Ref. 48.

The uniformity of the nozzle flow at several sections along the nozzle has been reported in Ref. 49 usingstagnation pressure measurements. Results have shown a flow uniformity of σ = ±3.5% within the inviscidcore of the flow. These measurements have been compared with numerical results for the nozzle flow asillustrated in figure 15. The shape of boundary layer profiles is in good agreement with an SST k–ω model.This confirms the turbulent nature of the boundary layers along the nozzle walls.

0 500 1000 1500 2000 2500 3000

−200

0

200

distance from nozzle throat, mm

radia

l dis

tance, m

turbulent SST k−ω model experiments characteristic line based on the SST k−ω solution

Figure 15: Normalized stagnation pressure profiles in the Longshot contoured nozzle

Ref. 49 reported on the presence of a slight discontinuity in the nozzle contour at 204 mm from the throatlocation. The propagation of the weak disturbances introduced at this location can be approximated byfollowing a characteristic line. This might be correlated with some of the deviations observed in the crosssection profiles, especially at about half the nozzle length. Yet, the presence of this disturbance could not beconfirmed at the nozzle exit (neither measured nor observed). Whether it can be responsible for the lowerMach number reported remains unknown.

Free-stream noise levels associated with the wind tunnel have been partially characterized in Ref. 49based on stagnation pressure fluctuations. A first approximation of the turbulence levels was determinedfor one operating condition (commonly referred to as “Low” Reynolds number). Even though the design ofthe probes may have introduced resonance effects leading to a slight overestimation, the standard deviationof the stagnation pressure fluctuations was measured as ±7.5%. Slightly lower amplitudes were observedat larger free-stream unit Reynolds numbers. The frequency response of the probes was limited to about20 kHz and no spectrum of the free-stream disturbances is therefore available yet.

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IV.C. Longshot conical model geometry and instrumentation

Transition studies have been performed in the Longshot wind tunnel using an 800 mm long 7 ◦ half-angle cone.The final surface quality is characterized by Ra < 3.2 µm. Six exchangeable nosetips ranging from 0.05 mmto 10 mm radii can be mounted on the model as illustrated in figure 16. With respect to the base radius RBof the cone, this corresponds to variations between 0.002 ≤ RN

RB≤ 0.1. Noses are made of stainless steel in

order to withstand the expected large stagnation point heat fluxes. The downstream sections of the coneare manufactured out of Aluminum.

Figure 16: Nosetips (0.05 mm, 0.2 mm, 0.75 mm, 1.75 mm, 4.75 mm, and 10 mm radii) and available instru-mentation locations along the 800 mm long 7 ◦ half-angle cone (thermocouples , Kulite pressure sensors ,PCB pressure sensors )

The cone is fitted partially within the contoured nozzle, in its inviscid uniform part as characterized inRef. 49. Only its most rearward part (between 110 and 225 mm depending on the configuration used) isextending out of the nozzle and allows for a limited flow visualization.

The angle of attack and sideslip of the model were both set to zero. Nosetips were exchanged successivelyfrom 0.05 to 10 mm radii. The wall to total temperature ratio varied between 0.16 ≤ Tw/Tt1

≤ 0.29.Only one side of the cone is instrumented along three main generatrices. The instrumentation includes

21 streamwise fast response type-E thermocouples, 7 streamwise piezoresistive Kulite XCE-093-5psi pressuresensors, and 8 piezoelectric pressure sensors PCB 132A31 at various locations as illustrated in figure 16. Allsensors are held in position from the inner parts of the cone in order to minimize the disturbances introducedat the surface.

Thermocouples are used to determine the wall heat flux distribution along the cone, from which thetransition extent can be inferred. Absolute pressure sensors have essentially been used to confirm the free-stream flow properties determined with the static pressure probe. Although not reported here, an excellentagreement has been obtained. Finally, piezoelectric pressure sensors are used to measure the boundarylayer disturbances along the cone. They are flush-mounted to the conical surface and were arranged in thestreamwise direction for tests reported here.

Further details about the experimental setup, the instrumentation used as well as some preliminaryresults can be found in Ref. 40.

IV.D. Transition location and nosetip bluntness effects

IV.D.1. Wall heat flux distributions

Wall heat flux distributions along the cone allow for an accurate and reliable definition of the transitionlocation. Stanton numbers for nosetip radii varying between 0.2–10 mm were reported in Ref. 40. Additionalexperiments have been performed since then for the sharpest nosetip available and results are reported infigure 17a for various free-stream unit Reynolds numbers.

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106

107

10−4

10−3

10−2

Reynolds number, Res, e

Sta

nto

n n

um

be

r b

ase

d o

n lo

ca

l q

ua

ntitie

s

laminar solution

turbulent solutionRe

unit, ∞=4×10

6/m

Reunit, ∞

=5×106/m

Reunit, ∞

=8×106/m

Reunit, ∞

=9×106/m

Reunit, ∞

=10×106/m

(a) 0.05 mm nosetip

106

107

10−4

10−3

10−2

Reynolds number, Res, e

Sta

nto

n n

um

be

r b

ase

d o

n lo

ca

l q

ua

ntitie

s

laminar solutionRe

unit, ∞=4×10

6/m

Reunit, ∞

=5×106/m

Reunit, ∞

=8×106/m

Reunit, ∞

=9×106/m

Reunit, ∞

=10×106/m

Reunit, ∞

=11×106/m

Reunit, ∞

=12×106/m

(b) 4.75 mm nosetip

Figure 17: Stanton number along a 7 ◦ half-angle cone as a function of the free-stream unit Reynolds number

The Stanton number initially decreases along the conical surface, following the Reynolds number de-pendence of the numerical laminar predictions, albeit 25% larger in all cases. The minimum heat transferlocation along the wall is defined as the transition onset, denoted by ResB, e, even if an accurate definitionof this location can be difficult with such discrete instrumentation.

The notable rise of the heat transfer coefficient after the transition onset corresponds to an increasinglyimportant intermittency factor of the boundary layer. A slight overshoot of the turbulent heat transfercoefficient predictions occurs at the end of the transition process. The maximum heat transfer locationalong the wall is then defined as the end of the transition region, denoted by ResE, e. The boundary layerthen approaches a completely turbulent state with a local heat transfer coefficient in better agreement withnumerical predictions and about 2.5 times larger than the laminar ones.

The transition delay trend observed on ResB, e in figure 17a while increasing the free-stream unit Reynoldsnumber is attributed to variations of free-stream noise levels as commonly reported in the literature.50–53

Figure 17b illustrates the strong stabilizing effect of nosetip bluntness on the boundary layer. With anosetip radius of 4.75 mm, an essentially laminar flow exists all along the cone with only a slight departurefrom the laminar trend for the largest local Reynolds number tested. With a larger 10 mm nosetip radius,the flow remained completely laminar40 at a free-stream unit Reynolds number of Reunit,∞ = 12 · 106 /m.

The stabilizing effect of nosetip bluntness is well illustrated by plotting the transitional Reynolds numberas a function of the Reynolds number based on the nosetip radius ReRN ,∞. This is illustrated in figure 18.Each symbol then represents the transition onset (i.e. departure from laminar trend), expressed here withrespect to free-stream quantities (ResB,∞) for comparison purposes with relevant literature.

Small amounts of bluntness do not significantly influence the transition onset location. This is indicatedby the curves drawn for similar free-stream conditions which are horizontal for small nosetip radii (RN =0.05–0.75 mm). On the other hand, as ReRN ,∞ increases beyond ReRN

& 4 000 , a significant transitiondelay is observed. With the 10 mm nosetip radius, transition onset ResB ,∞ is larger than 107 , i.e. at least2.5 times more than for the sharp configuration with the same flow conditions.

Data reported by Refs. 52, 54 for slender cones at slightly larger free-stream Mach number (12 to 15)are indicated on figure 18. The lower values for RexB,∞ reported here are a likely consequence of the largerhalf-angle cone used. For the same half-angle cone as the present one, results reported in Ref. 55 at lowerMach number but larger enthalpies actually fall within 10% of the present results for 3 500 . ReN . 35 000.They are not included in figure 18 for clarity.

Larger amounts of bluntness may stabilize the boundary layer further although transition reversal isexpected at some point. This regime could not be reached with the present flow conditions even for Reynoldsnumbers larger than ReRN,∞ = 120 000 for which the flow was still laminar at RB = 10RN .

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102

103

104

105

106

105

106

107

108

↑↑

Reynolds number based on nosetip curvature radius, ReR

N, ∞

Tra

nsitio

nal onset R

eynold

s n

um

ber,

Re s

B,

∞

Free−stream unit Reynolds number 1/m5e6 6e6 7e6 8e6 9e6 10e6 11e6 12e6 13e6

RN=0.05mm

RN=0.2mm

RN=0.75mm

RN=1.75mm

RN=4.75mm

RN=10mm

Reunit, ∞

≈12⋅106/m

Reunit, ∞

≈10⋅106/m

Reunit, ∞

≈6⋅106/m

Reunit, ∞

≈4⋅106/m

trend given by Softley (1969) at Reunit, ∞

≈4.92⋅106/m,

for a 5° half−angle cone

small bluntness(Softley 1968)

large bluntness(Softley 1968)

Figure 18: Effect of nose bluntness on the transition location (each nosetip radius is represented by a symboland its color is representative of the free-stream unit Reynolds number)

IV.D.2. Comparison with Pate’s correlation

10−4

10−3

10−2

105

106

107

CFII

Retr,δ

√

δ∗ C1 c

Pate’s correlation (1978)

original datasetR

N=0.05mm

RN=0.2mm

RN=0.75mm

Figure 19: Comparison with Pate’s correlation11

Nosetips smaller than 0.75 mm were shown in fig-ure 18 not to influence the transition location.They can therefore be assumed to be representa-tive of boundary layer transition on a sharp conegeometry and be compared to results obtained withPate’s correlation,11 based on the end of the tran-sition region. This correlation was developed basedon sharp cone results collected in 16 different windtunnels (from M∞ = 3 to 21) and indirectly ac-counts for the presence of radiated aerodynamicnoise through a characteristic nozzle wall skin fric-tion parameter.

Experimental results restricted to the equiva-lently sharp geometries are plotted in figure 19where CFII

is the nozzle wall skin friction coeffi-cient and the following parameters have been used:

• Longshot nozzle diameter is � = 0.426 m, giving Pate’s normalization parameter c = 0.9822,

• the distance between the throat and the leading edge of the model was varied between 2.31 − 2.42 m(the influence of this parameter on the transition location is very weak),

• the nozzle wall temperature varied between 292− 296 K among all tests,

• the Prandtl number was assumed equal to Pr = 0.713 and the recovery factor equal to r =√Pr,

• the nozzle wall skin friction coefficient was determined by the method presented in Ref. 6,

• the boundary layer displacement thickness along the nozzle wall was determined from Ref. 11,

• and the ratio of Reynolds numbers between the conical surface and the free-stream was interpolatedfrom Ref. 11.

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An excellent agreement is obtained between results obtained in the Longshot wind tunnel and the originalcorrelation. Scatter is comparable to the one observed in the original dataset. In order to get more insight intothe physics involved in this correlation, a better characterization of the free-stream noise levels is required.

IV.E. Spectrum of boundary layer disturbances and comparison with LST

Boundary layer disturbances have been measured along the surface using PCB 132A31 sensors. The powerspectrum of these fluctuations has been determined for each sensor using a wavelet analysis technique40

(based on a complex Morlet mother wavelet). An example for such a spectrum for a 1.75 mm nosetipgeometry (u∞ = 1689 m/s, T∞ = 69.5 K and p∞ = 277 Pa) is plotted in figure 20 against N -factors derivedfrom LST computations obtained with the the VESTA toolkit.35,40,56

frequency, kHz

Po

wer

Sp

ectr

alD

en

sity

Nfa

cto

r

0 100 200 300 400 50010

6

105

104

103

102

101

100

0

2

4

6

8

10

12

s=190mm

s=270mm

s=370mm

s=430mm

s=490mm

s=630mm

s=670mm

s=710mm

test 1763, t=10ms

M=10

Re=4.13x106/m

RN=1.75mm

Figure 20: Comparison between experimental data and VESTA computations (RN = 1.75 mm, M∞ = 10,Reunit,∞ = 4.13× 106 /m)

0 100 200 300 400 500 600 700 8000

1

2

3

4

5

6

s, mm

N f

acto

r

150 kHz

325 kHz

Figure 21: Transition location and corresponding N -factor for a conical geometry in the Longshot wind-tunnel (RN = 1.75 mm, M∞ = 10, Reunit,∞ = 4.13 ×106 /m)

Boundary layer disturbances grow in amplitudeas they flow along the cone from the first instru-mented location at s = 190 mm to the last one ats = 710 mm. Their dominant frequencies respec-tively shift from approximately 300 kHz down to180 kHz as the boundary layer thickens. For everylocation, the maximum amplitude frequencies are inexcellent agreement with the corresponding numer-ical predictions for Mack’s second mode.

Harmonics in the experimental signals corre-spond to non-linear interactions, not predicted byLST. Even though harmonics are present from s =490 mm, the agreement between experimental andnumerical data is still excellent until at least s =710 mm.

This remarkable agreement between experimen-tal and LST results is considered as an addi-tional proof that the method used in the Longshotwind tunnel to estimate free-stream conditions usingstatic pressure probes41 is accurate and well suitedfor hypersonic free-stream flow characterization.

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At the transition onset, determined from the minimum wall heat flux location as sB = 690 mm, thecorresponding N -factor is N = 5.0 (figure 21), which is well in line with lower Mach number conventionalhypersonic wind tunnels and similar to the N -factors reported in other Mach 10 wind tunnels.57,58 It isonly slightly lower than the one reported earlier for the H3 wind tunnel. This decrease can be expected fromthe fact that free-stream noise levels increase with the free-stream Mach numbers.29,30 Evaluation of thesensitivity of this N -factor to free-stream conditions and other geometries are under way.

IV.F. Flow visualization

IV.F.1. LIF-based Schlieren technique

A variant of the Schlieren flow visualization technique has been implemented in the Longshot wind tunnel,aiming at observing boundary layer disturbances. In order to freeze these high-velocity features in space, ashort duration laser has been used. The coherence of its light beam has been removed using an intermediatefluorescent dye plate (LaVision GmbH). This fluorescence was then used as the effective light source for anotherwise classical Schlieren setup.

Using a high repetition rate PIV laser allowed to obtain on the order of 50 image pairs per test, with aseparation time among an image pair ranging between 0.8–1 µs. Further details relative to the implementationof this technique can be found in Ref. 59 while typical images with second mode disturbances and theirpreliminary analysis were reported earlier.40,60 Additional processing of these images is reported hereafterwith the determination of the group velocities and the spectrum of the disturbances across the boundarylayer.

IV.F.2. Group velocities

The group velocities of the disturbances present in the boundary layer can be determined for each pair ofimage thanks to the short separation time. Preliminary results have been reported in Ref. 60 using PIValgorithms with small windows in order to determine convection velocities at different heights through theboundary layer. This proved to be difficult because of the integration of density gradients all along thelight path over such an axisymmetric configuration. 2-dimensional cross-correlation algorithms based on theentire images rather than on small windows are preferred here. This allows to determine the mean groupvelocity of the waves within the field of view and reduces the scatter of the results.

An example of image pair is displayed in figure 22. The slight displacement of the structures after 1 µsis indicated by reference arrows. Knowing the image resolution, the main group velocity of the disturbancesis estimated.

? ? ? ?

? ? ? ?

Figure 22: Example of image pair (RN = 1.75 mm), separation time 1 µs

The same automatic procedure has been repeated for each image pair where boundary layer disturbanceswere visible. Results are reported as red symbols in figure 23 for a transitional boundary layer over a1.75 mm nosetip radius cone and compared to the local flow velocity.

The decaying trend is evident with instantaneous values slightly lower than the local flow velocity. Asthe free-stream unit Reynolds number decays, disturbances within the boundary layer have lower amplitudesand are more difficult to track after about 7 ms. These values are compared to the results reported in Ref. 40based on the analysis of wall pressure measurements (blue dots). Both techniques were synchronized to eachother so that the reason for the lower group velocities determined from flow visualization remains unclear.

IV.F.3. Disturbances across the boundary layer

A frequency analysis of the light intensity distribution in each image has been performed in order to de-termine the location of the maximum amplitude disturbances within the boundary layer. Light intensity

15 of 26


0 2 4 6 8 10 12 14 16 18 200

500

1000

1500

2000

2500

time, ms

Velo

city, m

/s

cross−correlation of wall pressure data

cross−correlation of Schlieren images

free−stream velocity

theoretical BL edge velocity1±1/M

e

Figure 23: Group velocities for a transitional boundary layer (nosetip radius RN = 1.75 mm, 10.8 & M∞ &9.4 and 5.8 · 106 /m & Reunit,∞ & 3.4 · 106 /m)

profiles along pixel rows at several heights above the surface have been considered independently from eachother. Fast Fourier transform are then applied to each of these profiles to determine the wavelength of thedominant disturbances. Wavelength spectra are finally converted to approximated frequency spectra assum-ing a convection velocity of the disturbances equal to the local flow velocity (obtained from a Taylor-Maccollsolution).

Sample images where second mode waves are clearly visible are given in figure 24a. The FFT analysisperformed on each of these images, as a function of the wall distance, is then given in Figs. 24b to 24e,respectively. Images were equalized so that, even though vertical scales are identical, the respective amplitudeof peaks for different images is only qualitative.

This analysis is qualitatively comparable to the spectra obtained from hot-wires probes traversed throughthe boundary layer.34,61,62

Low frequency content is unlikely to be physical and rather represents background light variations alongan image row. Frequencies below 100 kHz were limited in their maximum amplitude for the present display.

Large amplitude disturbances at frequencies about 200 kHz correspond to second mode waves. This isin good agreement with frequencies reported earlier in figure 20 for similar free-stream conditions over thesame geometry and the back of the cone.

The edge of the boundary layer can be estimated from the location where no significant energy contentis present in the power spectrum. The inviscid part of the shock layer is essentially free from energy contentfor such a boundary layer. Based on the analysis of several images, the maximum amplitude fluctuationsoccurred in the outer part of the boundary layer between 0.55–0.65δ which compares well with values reportedin Ref. 63 using an analogous optical technique. Using hot-wires, which are sensitive to mass flow and totaltemperature fluctuations, Ref. 34, 61 have shown the maximum amplitude of the disturbances to occur atlocations closer to the edge of the boundary layer. Ref. 64 further report values close to 88% of the boundarylayer thickness. These differences might be due to the different definitions used to estimate the boundarylayer thickness.

Lower amplitude harmonics are also visible at higher frequencies. Their maximum amplitude occurs atabout the same height in the boundary layer than the main disturbances. It is questionable whether theseharmonics are related to the ones measured at the wall or not. They appear in these images once a clearrope shape of the waves is visible, i.e. once the curvature of the waves close to the boundary layer edge ispronounced. In these conditions, light intensity profiles chosen at heights which are in between the crestsand valleys of the second mode waves, exhibit wavelengths which are halved and harmonics are thereforeintroduced.

Two rows of pixels were included in this analysis although corresponding to locations below the surfaceof the cone. Close to the wall, fluctuations are vanishing unlike the results reported in Ref. 65. This has

16 of 26


5mm

wall

5mm

wall

5mm

wall

5mm

wall

(a) Images used for FFT analysis presented below, s = 595–770 mm

0

200

400 0

2

4

6

Distance fromthe wall, mm

Frequency, kHz

Pow

er

spectr

al density

(b) M∞ = 10.2, Reunit,∞ = 4.5 · 106 /m

0

200

400 0

2

4

6


Frequency, kHz

Pow

er

spectr

al density

(c) M∞ = 10.3, Reunit,∞ = 4.7 · 106 /m

0

200

400 0

2

4

6


Frequency, kHz

Pow

er

spectr

al density

(d) M∞ = 10.7, Reunit,∞ = 5.4 · 106 /m

0

200

400 0

2

4

6


Frequency, kHz

Pow

er

spectr

al density

(e) M∞ = 10.7, Reunit,∞ = 5.5 · 106 /m

Figure 24: FFT analysis of typical disturbances across the boundary layer (RN = 1.75 mm)

17 of 26


been observed for every image of the large set available. Image pre-processing was limited to a backgroundsubtraction using a reference light intensity distribution, equalization and the adjustment of saturation andgamma exponent. This is believed to have a limited influence on the present spectral results. The amplitudeof the disturbances is therefore expected to increase from the wall up to their maximum at y

δ ≈ 55–65%before rapidly decaying to weak amplitudes beyond the edge of the boundary layer.

IV.G. Comparison between different measurement techniques

IV.G.1. Overview

Different measurement techniques, synchronized to each other, have been used to characterize the boundarylayer transition process over Mach 10 in the Longshot facility. The present section compares wall heat fluxdistributions with Lif-based Schlieren images, standard deviation of surface pressure fluctuations along thecone and spectra of boundary layer fluctuations.

Measurements were considered over a short time window of ±1 ms during which free-stream conditionscan be regarded as approximately constant and quasi-steady. Schlieren images represent consecutive framescentered on that time window with a total duration of 0.8 ms. They serve to illustrate the intermittency ofthe waves within the boundary layer.

The end of the transition location is also compared to Pate’s correlation (this prediction is based on therelevant free-stream flow conditions for each case considered and assumes sharp cone geometries). Nosetipbluntness benefits are then easily appreciated.

Four cases are considered, giving an overview of the influence of nose bluntness and local Reynolds numberon the transition phenomenon at large hypersonic Mach numbers. They are as follow:

• A (sharp) nosetip of 0.75 mm with Reunit,∞ = 5 · 106 /m (figure 25),

• A (slightly blunt) nosetip of 1.75 mm with Reunit,∞ = 5 · 106 /m (figure 26),

• A (slightly blunt) nosetip of 1.75 mm with Reunit,∞ = 10 · 106 /m (figure 27),

• A (blunt) nosetip of 4.75 mm with Reunit,∞ = 10 · 106 /m (figure 28).

IV.G.2. Sharp cone

A nosetip of 0.75 mm can be assimilated to a sharp one since it does not delay transition (figure 18).For the conditions reported in figure 25, transition onset occurs at sB ≈ 490 mm (as inferred from the wall

heat flux distribution). The end of transition occurs approximately at sE ≈ 750 mm. This is in remarkableagreement with Pate’s correlation, which predicts the end of the transition location at sE,Pate ≈ 747 mm.

The evolution of the standard deviation of the pressure fluctuations during the transition is also indicated,each point corresponding to a PCB sensor. Even though the instrumentation is discrete, the peak of pressurefluctuations can be associated to the beginning of the transition region, defined from the rise of the wall heatfluxes. Disturbance spectra indicates that this corresponds to the maximum amplitude of the second modedisturbances, just before their breakdown. Such measurement techniques were also compared earlier on atMach 6 and in Ref. 57: the peak of wall pressure fluctuations were found to occur closer to the middle ofthe transition region, although the scarce instrumentation may have introduced some uncertainties.

The heat flux rise is then associated with the energy filling of the entire spectrum. Note that harmonicsare detected in the wall pressure traces at s ≈ 270 mm, i.e. long before the transition onset.

Flow visualization images depict the early development of turbulent structures within the boundary layerwith second mode waves limited to the left-hand side in few of the images. The field of view corresponds tolocations where the wall heat transfer is rising. This is closely similar to the conclusions reported in Ref. 52.

IV.G.3. Slight nose bluntness

For similar free-stream conditions but a slightly blunt nosetip, the wall heat flux rise is delayed and the endof the transition region occurs beyond the end of the cone (figure 26). Pate’s correlation does not accountfor the effect of nose bluntness but the nosetip stabilizing effect is evident.

The peak pressure fluctuations are again associated with the onset of transition sB , where wall heat fluxesare rising and the spectrum is filling up. Wall pressure fluctuation spectra indicate harmonics relatively earlyin the measurements, from about half way the extent of the laminar boundary layer.

18 of 26


Second mode wave trains are well visible from the Schlieren images in such conditions. They disappearshortly beyond the transition onset location sB . The intermittency of the boundary layer is clearly visiblefrom this series of images where rather laminar boundary layer alternates with wave packets. The right-handside of the images, located approximately half-way of the transition extent, is on the other hand, essentiallyturbulent.

IV.G.4. Slight nose bluntness at larger local Reynolds number

The same geometry at a larger local Reynolds number allows to obtain a fully turbulent boundary layer overthe cone (figure 27). The slight transition delay due to nosetip bluntness is appreciated by comparing themaximum wall heat flux location with predictions from Pate’s correlation. The characteristic overshoot atthe end of the transition region is also well detected.

The peak of the standard deviation of the wall pressure fluctuations is not as clear as for the previous casesreported. It however increases during the transition process and remains relatively large below a turbulentboundary layer.

The field of view of the Schlieren images is located slightly more downstream than previously. In combi-nation with a larger free-stream unit Reynolds number, images illustrate a fully turbulent boundary layer.Spectra associated to sensors within this field of view confirm the turbulent nature of the boundary layerwith noise being radiated towards the shock layer.

Even though the free-stream unit Reynolds number is twice larger than in the previous case (figure 26),the transition location sB is not exactly halved. This is due to the influence of the free-stream noise levels andthe characteristic free-stream unit Reynolds number effect which contributes to slightly delay the transitionlocation (figure 18) in ground facilities.

IV.G.5. Large nose bluntness

A larger nosetip radius of 4.75 mm delays the transition onset beyond the end of the cone (figure 28). Theincreasing stabilizing efficiency of the nosetip bluntness can be judged from the predictions for a sharp coneobtained from Pate’s correlation.

Even though the boundary layer seems laminar, disturbances are already present in the boundary layeras indicated by the Schlieren images. Disturbance spectra also reveal growing disturbances at about 200 −230 kHz and harmonics are detected for the last measuring stations. The low standard deviation shows thatthe flow would probably remain laminar for a little longer before reaching transition onset.

V. Conclusions

The recent flow characterization in two hypersonic wind tunnels of the VKI has been reviewed. In theH3 Mach 6 wind tunnel, emphasis was placed on the determination of the free-stream noise levels usingstagnation pressure probes and double hot-wires. The average amplitude for normalized Pitot pressurefluctuations is on the order of 1.7% while turbulence levels for the entropy, vorticity and acoustic modes,obtained from combined analysis, are on the order of 0.8%.

Boundary layer transition experiments on a 7 ◦ half-angle cone without angle of attack were then per-formed in this wind tunnel. Instrumentation included infrared and wall pressure measurements. Transitionlocations were determined for various free-stream conditions and comparison of the different measurementtechniques indicates a peak of wall pressure fluctuations in the middle of the transition region as defined fromlocal heat transfer measurements. The spectrum of boundary layer disturbances compares favorably withtheoretical results, confirming the second mode nature of the disturbances observed. The N -factor of theH3 wind tunnel is inferred from these comparisons and is about 5.5, as for similar conventional hypersonicwind tunnels.

In the Longshot wind tunnel, efforts were directed towards an improved free-stream flow characteriza-tion using static pressure probes. The new rebuilding procedure implemented relies only on measurementsperformed in the test section in order to characterize the hypersonic flow. This alleviates the need for reser-voir measurements and the following questionable isentropic and adiabatic expansion assumptions along thenozzle. This procedure uncovered a lower free-stream Mach number than expected from the nozzle design,albeit for reasons still under investigations.

19 of 26


0 100 200 300 400 500 600 700 800

0

0.2

0.4

0.6

0.8

1x 10

−3

Distance along the axis of the cone, mm

Sta

nto

n n

um

ber

Pa

te’s

pre

dic

tio

n

laminar trend

turbulent trend

experiments

qmin

qmax

transition extent

PCB sensors

s = 650mm 700mm 750mm

0 100 200 300 400 500 600 700 8000

0.1

0.2

0.3

0.4


Sta

ndard

devia

tion p

w’/p

w

40 60 80 100 200 300 400 600 800 100010

−6

10−4

10−2

100

frequency, kHz

Pow

er

Spectr

al D

ensity

sensor at:

s=190mm

s=270mm

s=370mm

s=430mm

s=490mm

s=630mm

s=670mm

s=710mm

Figure 25: Transition process over the 0.75 mm nosetip cone with different measurement techniques (M∞ =10.7, Reunit,∞ = 5 · 106 /m)

20 of 26


0 100 200 300 400 500 600 700 800

0

0.2

0.4

0.6

0.8

1x 10

−3


Sta

nto

n n

um

ber

Pa

te’s

pre

dic

tio

n

(assu

min

gsh

arp

co

ne

)

laminar trend

turbulent trend

experiments

delay dueto bluntness

qmin

PCB sensors

s = 650mm 700mm 750mm

0 100 200 300 400 500 600 700 8000

0.1

0.2

0.3

0.4


Sta

ndard

devia

tion p

w’/p

w

40 60 80 100 200 300 400 600 800 100010

−6

10−4

10−2

100

frequency, kHz

Pow

er

Spectr

al D

ensity

sensor at:

s=190mm

s=270mm

s=370mm

s=430mm

s=490mm

s=630mm

s=670mm

s=710mm


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0 100 200 300 400 500 600 700 800

0

0.2

0.4

0.6

0.8

1x 10

−3


Sta

nto

n n

um

ber

Pa

te’s

pre

dic

tio

n

(assu

min

gsh

arp

co

ne

)

laminar trend

turbulent trend

experiments

qmin

qmax

transition extent delay dueto bluntness

PCB sensors

s = 650mm 700mm 750mm 800mm

0 100 200 300 400 500 600 700 8000

0.1

0.2

0.3

0.4


Sta

ndard

devia

tion p

w’/p

w

40 60 80 100 200 300 400 600 800 100010

−6

10−4

10−2

100

frequency, kHz

Pow

er

Spectr

al D

ensity

sensor at:

s=190mm

s=270mm

s=370mm

s=430mm

s=490mm

s=630mm

s=670mm

s=710mm

Figure 27: Transition process over the 1.75 mm nosetip cone with different measurement techniques (M∞ =11, Reunit,∞ = 10 · 106 /m)

22 of 26


0 100 200 300 400 500 600 700 800

0

0.1

0.2

0.3

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0.5


Sta

nto

n n

um

ber

Pa

te’s

pre

dic

tio

n

(assu

min

gsh

arp

co

ne

)

laminar trend

experiments

x 10−3

delay dueto bluntness

PCB sensors

s = 650mm 700mm 750mm 800mm

0 100 200 300 400 500 600 700 8000

0.1

0.2

0.3

0.4


Sta

ndard

devia

tion p

w’/p

w

40 60 80 100 200 300 400 600 800 100010

−6

10−4

10−2

100

frequency, kHz

Pow

er

Spectr

al D

ensity

sensor at:

s=190mm

s=270mm

s=370mm

s=430mm

s=490mm

s=630mm

s=670mm

s=710mm


23 of 26


A conical model similar to the one used in the H3 wind tunnel was then tested in the Longshot facilityat Mach 10. Instrumentation at the wall includes thermocouples and fast-response pressure sensors. Thestabilizing effect of nosetip bluntness has been demonstrated up to moderate amounts of nosetip bluntness.No transition reversal could be observed at RB = 10RN for a Reynolds number based on the nosetip radius ofReRN ,∞ = 120 000. Experimental results of the end of the transition region are in remarkable agreement withpredictions from Pate’s correlation. Spectra of boundary layer disturbances are in excellent agreement withLinear Stability Theory results obtained with the VESTA code and indicates the dominance of second modewaves at Mach 10. An N -factor of 5 was inferred for these experiments. Schlieren flow visualization confirmsthe presence of second mode waves within the boundary layer. The spectrum of boundary layer disturbancesacross the boundary layer has been determined from image analysis and indicates a peak of fluctuations atabout 0.6δ. Comparison of the different measurement techniques were finally reported, indicating a peakof wall pressure fluctuations corresponding with the onset of the boundary layer transition region. Thesaturating amplitude of the second mode waves corresponds to their breakdown and is closely related to thetransition onset location. Schlieren images depict intermittent second mode waves prior to the transitiononset location before breaking down, in agreement with results inferred from the wall. Additional analysis isstill on-going for the latter extensive dataset acquired for different nosetip bluntness and different free-streamconditions.

Acknowledgments

The authors gratefully acknowledge FRIA (Fonds pour la formation a la Recherche dans l’Industrie etdans l’Agriculture) for the financial support of this project. Best thanks are due to Steve Vanlanduit andAlexandru Nila (Vrije Universiteit Brussel) for the loan of their ILA High Speed PIV system. The authorsalso thank Dr. M. Choudhari who performed stability computations using the LASTRAC 3D code andDr. F. Pinna for the Linear Stability Theory results obtained with the VESTA toolkit.

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Flow characterization and boundary layer transition