Disturbance-Level and Transition Measurements in a

Conical Boundary Layer at Mach 6

Dirk Heitmann∗, Christian Kahler† and Rolf Radespiel‡

Institute of Fluid Mechanics (ISM), Technische Universitat Braunschweig

Bienroder Weg 3, 38106 Braunschweig, Germany

Tim Rodiger∗, Helmut Knauss§ and Ewald Kramer¶

Institute of Aerodynamics and Gas Dynamics (IAG), Universitat Stuttgart

Pfaffenwaldring 21, 70550 Stuttgart, Germany

Boundary layer transition on a 7 deg half-angle cone at zero angle of attack was studiedin combination with disturbance level measurements in the Hypersonic Ludwieg Tube ofTechnische Universitat Braunschweig. The disturbance level was not only determined bymeans of pitot-pressure fluctuations but also by fluctuation of heat flux in the stagnation-point using a fast-response heat-flux gauges. In addition, the second-mode instability wavesin the conical boundary layer were detected by a streamwise array of surface-mountedheat flux gauges with a spectral resolution up to 1 MHz. Simultaneous measurements ofthe disturbance level during all runs allows a comparison of the spectral distributions ofnormalized wave amplitudes on the surface and in the stagnation point. Furthermore theeffect of local roughness elements on the transition scenario was examined.

I. Introduction

The transition from laminar to turbulent in hypersonic boundary layers (BL) is important for the pre-diction of friction and heat transfer on the surface of flight vehicles. Despite of extensive research in

the last decades the mechanisms leading to transition are not yet completely understood. While empiricalprediction models are available models based on the growth and breakdown of disturbances in the boundarylayer are not on-hand. Because of this, the influence of several parameters, such as leading-edge radius, angleof attack, surface to free-stream temperature-ratio, free-stream turbulence etc. are not well understood. Inhypersonic flows the transition of the cone at zero angle of attack is dominated by the second-mode wavesdescribed by Mack.1 Several measurements of the second-mode instability have been carried out in the pastwith various measurement techniques, e.g. hot wires, heat flux or pressure gauges etc.The disturbance level of the hypersonic facility is of great importance for transition measurements as shownby Laufer.2 Especially for measurements of instability waves the free-stream disturbance spectra of thefacility are of importance. Commonly, the disturbance level is documented by normalized pitot-pressurefluctuations representing the acoustic noise that is radiated from the turbulent BL on the nozzle walls. Here,the disturbance level was additionally measured by means of fluctuations of heat flux in the stagnation pointthat ought to correlate with total temperature fluctuations in the driver tube.

∗Research Assistant.†Head of work group ”Flow Control and Measuring Techniques”.‡Professor. AIAA Senior Member.§Senior Scientist. Former Head of High-Speed Laboratory. AIAA Member, retired.¶Professor AIAA Member.

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26th AIAA Aerodynamic Measurement Technology and Ground Testing Conference<BR>23 - 26 June 2008, Seattle, Washington

AIAA 2008-3951

Copyright © 2008 by Dirk Heitmann. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

The flow quality has an influence on the transition Reynolds number and transition scenario on models. Inthis paper, the transition on a 7 deg. half-angle cone at zero angle of attack with a sharp nose is studiedby surface mounted heat flux gauges. The spectral range and amplitudes of the second-mode waves in theearly stages of transition are measured using an array of these heat flux sensors. Signal conditioning oftheir output allows the simultaneous detection of mean value and fluctuations close to the model surface.Hence, quantitative comparison of the spectral distributions of disturbance level and surface fluctuations arepossible. The non-intrusive character of such surface-mounted techniques is an important issue. Therefore,the influence of the local roughness elements created by a planar sensor module in the cone model surfaceis investigated by means of detected distortions in the development of the spectral disturbance distributionand calculation of Reynolds number based on the maximum roughness height created by the modules.

II. Experimental Setup

II.A. Facility

The Hypersonic Ludwig tube (HLB) of Technische Universitat Braunschweig has been described previ-ously.3, 4 The HLB is a wind tunnel that runs at a nominal Mach number Ma∞ = 6 in a unit Reynoldsnumber range of [3 − 20] · 106 /m for about 80 ms at conventional noise level. The driver tube of the HLBis separated from the low pressure section, consisting of nozzle, test section, diffuser and a dump tank, by afast-acting valve. The driver tube is heated along the first 3 m upstream of the valve. The heated sectionaccommodates the amount of gas that is released during one run. The valve consists of a streamlined centerbody on the tube axis. The nozzle maintains an opening half angle of 3◦ which results in slightly expandingflow in the test section with Mach numbers between 5.8 and 5.95 depending on the axial position and onthe unit Reynolds number. The driver tube pressure is recorded with an accuracy of ±1%. The driver-tubetemperature is measured during the run. It must be noted that the measured temperature difference be-tween the upper and lower measurement position can be as high as 30K due to temperature stratification.The mean value, however, is not proven to be the total temperature at the height of the model in the testsection. For the determination of the Reynolds number resulting from the uncertainties in total temperature,pressure and Mach number in the test section yield an overall uncertainty of about ± 2% in the relevantunit Reynolds number range. The disturbance level of the facility is examined in more detail in this paper.

II.B. Instrumentation

Fast-response heat flux sensors, called Atomic Layer Thermopile (ALTP), were used for fluctuations mea-surements on the surface and in the stagnation point of a blunt-body probe. The working principle of theALTP is based on the transverse Seebeck effect and the sensor allows for measurements of heat flux densityfluctuations up to 1 MHz. The output signal is directly proportional to the heat flux density in the rangeof interest. The active area of the sensors applied in this experiments is 2.0 × 0.4 mm2 and their sensitivityis between 75 and 100 μV/(W/cm2). The ALTP signal is amplified by special custom-made miniaturizedlow-noise amplifiers (COSYTEC) with adjustable gain from 10 to 10,000 for the low-pass filtered signal anda fixed amplification rate of 5,000 for the high-pass filtered signal. The housing of the sensor modulus ismade of a ceramic insulator (MACOR) and has a flat circular surface with a diameter of 8 mm. For furtherinformation the reader is referred to Roediger, Knauss et al.5, 6

In addition, the amplitude-frequency response (AFR) characteristics of the measurement system is taken intoaccount in order to determine absolute values of wave amplitudes. The AFR characteristics are measured bydynamic laser beam calibration using the modulated output of a diode laser in a frequency range between 1kHz and 1 MHz. A more detailed description of the dynamic calibration procedure can be found in Knausset al.6 and Roediger et al.7 An Entran EPIH-113-1B/Z1 pressure transducer is used in the pitot pressureprobe. It has a measuring range of 50 psi, a natural frequency of 400 kHz and a flush-mounted membrane(1.5 mm in diameter). The manufacturer specifies the useful range as 20 % of the resonant frequency. The

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pitot-pressure fluctuations were furthermore measured with a PCB M131A32 sensor. The diameter of theactive area is 3.18 mm. The power was supplied by a PCB 482A22 instrument, which at the same timeperformed signal conditioning. The sensor has a sensitivity of 140.5 mV/psi. The natural frequency of thissensor is specified by the manufacturer to above 1 MHz. These excellent dynamic properties are of specialinterest for pitot pressure fluctuations, although the sensor only measures fluctuations and the spectra cannot be normalized.

II.C. Stagnation Point Probes

The pitot probe consists of a 7.5 mm diameter reference tube with a 15◦ conical head and a planar surfacewith a diameter of 5 mm. The Entran EPIH-113-1B/Z1 pressure gauge is flush mounted in the planar frontsurface and ground insulated in the head of the pitot probe. The stiffness of the probe is enlarged by meansof a conical shaped tube socket at the top end.8

The stagnation point heat flux fluctuation measurements are carried out by blunt bodies with a basediameter of 20 mm. The shape of the body head was specially designed for such stagnation point measure-ments. It has a planar front surface of 10 mm in diameter and an elliptical contour in order to achieve aplateau of constant heat flux density in the stagnation region.9, 10 The ALTP gauge is flush mounted in theplanar front surface insulated by a ceramic (MACOR) casing in order to avoid lateral heat conduction.

II.D. Cone Model

A 7◦ half-angle cone of 500 mm in length and a sharp nose tip was used for the experiments. The model ismade from aluminium. The tip of the cone is made from steel to achieve higher manufacturing tolerances.The cone permits the installation of heat flux gauges at 14 different locations along a generator of the cone,starting at a distance of 100 mm from the tip with a spacing of 25 mm. (Fig. 1). Contoured blind stoppersreplace unused gauge positions of the model. The ALTPs have a circular planar surface of 8 mm in diameter,i.e. a local roughness is created, with the dimension depending on the position of the gauge in reference tothe cone tip and the manner of the installation. The gauges in the experiments were installed in the midpart of the cone between 270 and 345 mm from the tip. The sensors could either be flush mounted on thesides, thus creating a cavity (this cavity is shown exemplarily in Figure 1b for a position 150 mm from thetip) or they could be mounted flush on front and rear side, thus creating protrusion on the sides. In thepresent experiments the middle between these positions was chosen, i.e. a small cavity along the centerlineand a small protrusion on the sides of the gauges were created. Different blind stoppers were used as localroughness elements with a diameter of 8 mm with flat and contoured surface by means of a mechanicaldisplacement mechanism, as well. The cone was aligned to zero angle of attack by measuring the line oftransition with an infrared camera. The alignment was attained iteratively in subsequent tunnel runs untilthe transition line was found to be straight.

II.E. Data Analysis

Data Acquisition and Processing. The ALTPs and the pressure gauge signals were sampled with aSpectrum M2i.4652 transient recorder. The sampling rate was set to 3 MHz and the data was stored ina 16 bit format. Time traces of about 265 ms were captured for the ALTP and pressure gauge signals,consisting of about 180 ms before and 80 ms during the tunnel run. Electrical noise from the fast reactingvalve disturbed the ALTP time trace and divided the measuring time into sequences of 30-40 ms duringa single run. The resulting heat flux signals were divided into windows of 600 data points (0.2 ms). Thewindows overlapped with 400 data points, resulting in 450 to 600 windows. These windows were multipliedwith a normalized Blackman window, Fourier transformed and averaged over all windows. The uncorrelatedelectronic background noise was reduced by subtracting the power spectra of a time trace measured prior toeach tunnel run. When this subtraction yielded negative values these were set to zero.

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(a) Measurement positions on the cone model (b) Roughness of ALTP in cone model

Figure 1. Cone model

Amplification rates. For the calculation of the amplification rate in x-direction, the relation given byMack1

−αi =(

1A

) (dA

dx

)(1)

with negative values of αi denoting amplification, was simplified for the calculation of the amplification ratesbetween single-point sensors. If αi is constant, exponential amplitude growth can be assumed leading to

−αi = ln(A2/A1)x2−x1

if A1 > 0 and A2 > 0−αi = 0 else

with A1 and A2 being the wave amplitudes after noise subtraction at two consecutive sensors and (x2 - x1)being the surface distance between those sensors.It must be noted, however, that the assumption of constant αi is only of limited validity because the distancebetween the sensors is fairly large and several times the wavelength of the investigated instability waves.

III. Experimental Results

III.A. Determination of HLB Disturbance Level

Commonly, the disturbance level of a hypersonic test section flow refers first and foremost to the so-called“acoustic mode”, i.e. sound waves which are detectable as pressure fluctuations. Most of these sound wavesare emanating from the turbulent boundary layer (BL) of the nozzle and test section wall. Consequently,they correlate in intensity and spectral distribution with the BL characteristics like thickness, Mach numberetc.11 Therefore this acoustic mode is Reynolds number dependent and can cause a unit Reynolds numbereffect in wind tunnel transition experiments. Pitot pressure fluctuations are mostly used as a representativequantity although according Stainback and Wagner12 such dynamic pitot pressure measurements appear tobe limited to qualitative indications of the acoustic disturbance level and trend in a given facility. Onlyhot wire anemometry with the “fluctuation diagram” technique by Kovasznay13 and Morkovin14 allows amore complete detection and differentiation of possible existing disturbance modes which imply also the“entropy mode” i.e. total temperature fluctuations. In order to obtain some information about this kindof disturbance mode, the ALTP heat flux sensor is used for the detection of heat flux density fluctuations(HFF) in the stagnation flow which correlate with the total temperature fluctuation15 in the oncoming freestream. Total temperature fluctuations are only sparsely determined for the qualification of test section

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flows in other supersonic and hypersonic facilities to the authors’ knowledge. Because of the fast frequencyresponse of the ALTP sensor, with a time constant 2 to 3 orders smaller than the one of hot wires, such aHFF measurement seems far promising. To the authors’ opinion, there is for the first time the possibility todetect temperature fluctuations in a frequency range not been accessible up to now.Figure 2 shows amplitude spectra of normalized pitot pressure fluctuations, at a unit Reynolds number of6.0× 106 /m at three positions in the vertical symmetry plane of the test section, where also the streamwisearray is located in the cone experiments presented later. All three pressure curves show a noticeable peak atabout 410 kHz, representing the natural frequency of the pressure gauge. A typical decay of the fluctuationlevel vs. frequency without considerable dominant peaks is visible. The rms values of the normalized pitotpressure fluctuations (defined as p′RMS/ppit) are between 1-1.6% and increase towards the centerline. Fig-ure 3 shows the amplitude spectrum of the heat flux fluctuation in the stagnation point of the blunt bodynormalized by the corresponding mean heat flux density obtained simultaneously. The curves show peaksat the frequencies 110, 190, 250 and 330 kHz. The rms values of the normalized fluctuations q′RMS/qSP arebetween 5.3-7.3% and increase towards the centerline, like the pressure fluctuations. A first reason for thisincrease in the center region is the known focussing effect of an axial symmetric nozzle, i.e all disturbancesthat have their origin in the contour of the nozzle are focussed towards the axis. This increase might alsoresult from wake remnants emanating from the fast reacting valve housing and a last possible reason for thisincrease might be a conical compression wave that is known to focus on the axis within the test section. Thepeaks in the HFF might originate either from an unstable detached shock wave in front of the probe or fromthe temperature stratification inside the driver tube (up to ∼30K).Figure 4 shows unnormalized spectra for runs with and without heating of the driver tube. These mea-surements were made with a high-frequency pressure sensor of type PCB M131A32 mounted in the bluntbody with elliptic shape like that used for the ALTP gauges. This sensor was chosen because of the limitedfrequency range of the Entran EPIH-113-1B/Z1 sensor (Fig. 2). For the tunnel run with driver tube heatingthe pressure sensor shows fluctuations similar to the HFF (see Fig. 3). The dominant frequencies are in goodagreement. The additional peak at ∼300kHz is believed to be sensor specific. Furthermore, the figure showsa spectrum measured in a tunnel run without heating of the driver tube and hence without temperaturestratification. The dominant frequencies did not vanish and are only shifted in comparison to the case withheating. The entire flow field is completely different for both cases, however, this result might indicate thatthe dominant frequencies could be originated from the shape of the blunt body instead of the temperaturestratification.Figure 5 depicts unnormalized pressure spectra measured with the same pressure gauge and with two dif-ferent blunt body shapes for the same nominal flow conditions. In contrast to the up to now used ellipticalshaped body, a 45◦ conical body with a planar surface of 5 mm was used. The spectrum for the conicalblunt body shows a single peak at 60 kHz instead of the multiple peaks as detected by the body with theelliptical contour. This completely different characteristic originates presumably from the different stabil-ity behavior of the detached shock wave of the blunt bodies. These results are only preliminary and needfurther systematic studies. The figures 2, 3 and 5 displayed only spectra for two unit Reynolds numbers.Due to the dependency of the disturbance level on the characteristic of the nozzle BL, an examination ofthe fluctuations for different unit Reynolds numbers is necessary. Figures 6 and 7 show pitot pressure andheat flux fluctuations for three different Re∞/l. These spectra were measured simultaneously to fluctuationsin the boundary layer of the cone, that are presented in the following section. The probes were mountedat a position 129 mm below the wind tunnel centerline, i.e. at a different position from that correspondingto the spectra of figures 2 and 3. Both quantities exhibit the same behavior like the fluctuations above thecenterline. The HFF (measured with the elliptical blunt body) show peaks at the same frequencies. Thenoise level, calculated from the normalized standard deviation of the pitot pressure time signal is in the rangeof 1.0 to 3.6 % with a mean of 1.67 %, depending mainly on the position is the test section. These valuesare a result of the entire measurement campaign and are not shown here. The pressure disturbance leveldepends on the unit Reynolds number with a slightly decrease towards increasing unit Reynolds numbers.This confirms the origin of these sound waves in the turbulent BL of the wind tunnel walls. Such a trend

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f [kHz]

(p’/p

) pit[-

]

0 100 200 300 40010-6

10-5

10-4

10-3

10-2

10-1

065129

Re∞/l ≈ 6 × 106 1/mx = middle of test section

z [mm] (p’RMS/p)p

1.6281.2611.026

Figure 2. Spectra of normalized pitot pressure fluctua-tions for Re∞/l ≈ 6 × 106/m

f [kHz]

(q’/q

) SP

[-]

0 100 200 300 400 50010-4

10-3

10-2

10-1

065129

Re∞/l ≈ 6 × 106 1/mx = middle of test section

z [mm] (q’RMS/q)SP [%]

7.3546.2875.346

Figure 3. Spectra of HFF in the stagnation point forRe∞/l ≈ 6 × 106/m

f [kHz]

p’[p

si]

0 100 200 300 400 50010-5

10-4

10-3

10-2

10-1

100

T0 ≈ 480 KT0 ≈ 300 K

p0 ≈ 5.5 bar

Figure 4. Spectra of pitot-pressure fluctuations with andwithout driver tube heating

f [kHz]

p’[p

si]

0 100 200 300 400 50010-5

10-4

10-3

10-2

10-1

100

p0 ≈ 5.5 barT0 ≈ 480 KRe∞/l ≈ [4.5 - 4.6] × 106 1/m

Figure 5. Spectra pitot pressure fluctuations for differ-ent probe bodies at Re∞/l ≈ 4.5 × 106/m

cannot distinctly be confirmed for the HFFs. The normalized rms value of the HFF is in the range of about5.4 % and no dependency on the unit Reynolds number can be noticed. The spectra show unambiguouslyan uncorrelation of both disturbance modes. It is obvious that the entropy mode also with a higher level ofintensity has its origin in the prehistory of the flow generation, i.e. in the driver tube, where a temperaturestratification distorts the homogeneity of the initial state determining the stagnation condition of the flow.A temperature difference of 40 K between upper and lower storage tube wall was measured. Such a spatialtemperature gradient will cause unavoidable convective vorticity and temperature fluctuations in the drivertube. These irregularities are convected by the nozzle flow into the test section. It is clear that these tem-perature fluctuations are not dependent on unit Reynolds number and hence, they do not correlate with theexisting pressure fluctuations.

Table 1 summarizes the noise level results obtained for the HLB and gives information about noise levelsof some other facilities.

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f [kHz]

(p’/p

) pit[-

]

0 100 200 300 40010-6

10-5

10-4

10-3

10-2

10-1

3.365.888.31

x = middle of test sectionz = -129mm

(p’RMS/p)piRe∞/l [Mio./m]

1.551.441.38

Figure 6. Spectra of normalized pitot pressure fluctu-ations for different Re∞/l measured simultaneously toHFF in a conical BL

f [kHz]

(q’/q

) SP

[-]

0 100 200 300 40010-4

10-3

10-2

10-1

3.365.887.48

x = middle of testsectionz = -129mm

(q’RMS/q)SPRe∞/l [Mio./m]

5.365.375.40

Figure 7. Spectra of HFF in the stagnation point fordifferent Re∞/l measured simultaneously to HFF in aconical BL

III.B. Circular Cone Experiments

In the following, hypersonic BL transition on a cone was studied using a streamwise array of ALTP heatflux gauges. Since the disturbance level is one of the most well-known influences on BL transition, the dis-turbance level of each single run was recorded simultaneously by the stagnation point probes as described inthe previous section. These simultaneous measurements allow the calculation of spatial amplification ratesin combination with the disturbance level recorded as normalized fluctuations of pitot pressure as well asheat flux density.In order to document the repeatability of the runs, Figure 8a shows typical amplitude spectra (AFR cor-rected) for two tunnel runs at the same nominal unit Reynolds number Re∞/l = 5.85×106 /m. The spectraclearly reveal the dominant second mode as peak in the frequency range between 150÷300 kHz at bothposition x=295 and x=345 mm. Despite of a slightly lower maximum amplitude of the second mode at bothpositions in the first run, the agreement of calculated amplification rates (lower curves) is very good. Sucha discrepancy in amplitude can be explained by light variation of the initial disturbance level in the drivertube and test section. The simultaneous stagnation point measurements indicate such an effect - at least,the pitot-pressure fluctuations p′RMS/p are lower for the first run (while q′RMS/q remains approximatelyconstant). The disturbance level is given here as rms value in order to describe a certain trend. Yet thisquantity does not give any information on the spectral distribution and level of fluctuations in the relevantfrequency range. Such a spectral comparison will be discussed later (see Fig. 11).Figure 8b shows the amplitude spectra of all four ALTPs captured simultaneously during one single runat constant Re∞/l = 4.22 × 106 /m. The characteristic frequency shift of the second mode towards lowerfrequencies with increasing running length x and the rising amplitude at the same time is visible. Theamplification rates calculated between the distinct sensor positions (given in the legend) are shown in thelower part of the diagram. The growth rate calculated between the two most upstream sensors appear to besystematically higher than the ones calculated at downstream positions. However, it should be noted thatthe amplitude of the second mode was close to the background noise level for the measurement performedat these positions and such low unit Reynolds numbers of Re∞/l = 4.22 × 106/m. The amplification ratescalculated between the three upstream positions are in fairly good agreement.For a variation of unit Reynolds number, the transitional regime shifts successively across the gauges and

the amplitude spectra can be assorted to characteristic contours showing the different stages of transitionand second mode growth and decay. Figure 9 displays such a “footprint” for the fixed sensor positionx = 345 mm. For each single spectrum forming the contour (vertical lines), the simultaneously measured

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f [kHz]

q’[W

/cm

²]

-αi[1

/m]

0 100 200 300 400 500-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0

20

40

x = 295mm

x = 345mm

Re∞/l ≈ 5.85 × 106 1/m (p’RMS/p)pit

[%]

1.351.44

5.385.37

(q’RMS/q)SP

[%]

(a) Spectra of HFF and spatial amplification rates (ALTPs at x = 295 and 345 mm) for twotunnel runs at same nominal conditions and simultaneously measured disturbance levels

f [kHz]

q’[W

/cm

²]

-αi[1

/m]

0 100 200 300 400 500

-0.02

-0.01

0

0.01

-50

0

50

100

150

x = 295 mm

x = 270 mm

x = 320 mmx = 345 mm

-αi; 270-295mm

-αi; 295-320mm

-αi; 320-345mm

(b) Spectra of HFF and calculated amplification for one single run at Re∞/l = 4.22 × 106/m

Figure 8. Spectra and amplification rates determined on the surface of the circular cone

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Table 1. Noise level of different wind tunnels

Wind Tunnel (p′RMS/p)Pit [%] (q′RMS/q)SP [%]HLB† Re∞/l = 6.0 Mio./m 1.03 5.35

Re∞/l = 12.8 Mio./m 0.94 5.04Boeing/AFOSR* quite mode 0.03 -

noisy mode 3.0 -AEDC Wind Tunnel No. 9♣ Mach 8 2.0 - 3.5 -

Mach 10 2.5 - 4.0 -Mach 14 3.75 - 6.25 -

ASU Supersonic Wind Tunnel♠ Mach 2.4-3.5 0.15 -SWK/IAG + Mach 2.5 0.1-0.15 -† measured at the middle of the testsection at Z = 129mm*Schneider et al., High-Reynolds-Number Laminar Flow in the Mach-6 Quit-Flow Ludwieg Tube, AIAA Paper2006-3056, 36th AIAA Fluid Dynamics Conference, San Francisco, CA, June 2006.

♣Lafferty, Norris, Measurements of Fluctuating Pitot Pressure, ”Tunnel Noise,” in the AEDC HypervelocityWind Tunnel No. 9, AIAA Paper 2007-1678, Destin, Florida, February 2007.

♠Zuccher, Saric, Infrared Thermography investigations in transitional supersonic boundary layers, DOI10.1007/s00348-007-0384-1, Experiments in Fluids, 2007.

+Weiss, J., Knauss, H., Wagner, S.Experimental Determination of Free Stream Disturbance Field in a ShortDuration Supersonic Wind Tunnel. Experiments in Fluids, 35, pp. 291-302, 2003.

disturbance level is given in the box. The top values are the normalized pitot-pressure fluctuations andthe lower values represent the fluctuations of stagnation-point heat flux. In Figure 9, the second mode isclearly visible between 150 and 200 kHz with increasing frequency for rising Reynolds number. The modecan be detected at a Reynolds number as low as ∼ 1 × 106. At a Reynolds number ∼ 2.25 × 106, the firstharmonic appears and both the lower and higher frequency portion of the spectrum starts to fill in. AtRe∞ ≈ 2.6 × 106, the amplitude of the second mode peak saturates. The fluctuations of stagnation pointheat flux remain as expected fairly constant within certain limits (q′RMS/q)SP = 5.3 − 5.4 for all runs. Thesame characteristic is observed for the pitot-pressure fluctuations (p′RMS/p)pit = 1.35 − 1.55. They wereexpected to slightly decrease with increasing unit Reynolds number (as shown in section III.A). However,the unit Reynolds number range covered was fairly small to clearly reveal this trend.Figure 10 displays amplification rates calculated from the ALTP amplitude spectra between positions x=295mm and x=345 mm (Fig. 9) for a variation of Reynolds number. The maximum amplification rate of−αi ≈ 20/m is obtained for a Reynolds number of Rex ≈ 2× 106. At higher Rex the maximum αi decreasesand a broader frequency range seems to be amplified. The quality of the data is insufficient to preciselycalculate an amplification rate in an extended frequency range above ∼300 kHz.So far, the rms values of pitot-pressure and stagnation-point heat flux were used to indicate the disturbancelevel within the test section. More important, however, is the spectral distribution of disturbances in the testsection. To compare wave amplitudes in the relevant spectral ranges on the cone surface and the disturbanceamplitudes measured in the stagnation point, Figure 11 shows the normalized fluctuations of measured heatflux (signal conditioning of the ALTP signal allows the detection of mean value and fluctuations simulta-neously). In the Figure, two heat flux spectra at the cone surface at two different Reynolds numbers arecompared to normalized fluctuations of heat flux in the stagnation point. The spectrum at Rex = 1.84× 106

is in close proximity to the saturation of second-mode amplitude.At low frequencies, the normalized fluctuation on the surface are by already a factor of 10 higher than

the one measured in the stagnation point. This effect is not clearly understood and rises questions of recep-

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Rex [-]

f[kH

z]

1.5x10+06 2.0x10+06 2.5x10+060

100

200

300

400

500

q’ [W/cm²]

0.060.0540.0480.0420.0360.030.0240.0180.0120.0060

p’RMS/ppit

q’RMS/qSP

1.38%6.29%

1.47%5.40%

1.49%5.59%

1.35%5.38%

1.39%5.32%

1.39%5.34%

1.55%5.36%

ALTP atX = 345 mm

Figure 9. HFF Spectra for fixed sensor position x = 345 mm) as contour for a variation of Re∞

Re∞/l [1/m]

f[kH

z]

4.0x10+06 5.0x10+06 6.0x10+06 7.0x10+06 8.0x10+06

0

100

200

300

400

500

αi [1/m]

201612840

-4-8-12-16-20

-αi calculated from spectra measured atx = 295 and 345mm

Rex [-]

f[kH

z]

1.5x10+06 2.0x10+06 2.5x10+060

100

200

300

400

500

αi [1/m]

201612840

-4-8-12-16-20

-αi calculated from spectra measured atx = 295 and 345mm

Figure 10. Spatial amplification rate calculated from spectra at x = 295 mm and x = 345 mm as contour for a variationof Re∞

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f [kHz]

q’/q

[-]

0 100 200 300 400 500

10-3

10-2

10-1

100

Re∞/l [Mio./m] Rex [Mio.] (q’/q)RMS [%]

5.88 - 6.55.74 1.55 42.05.74 1.84 71.3

close to saturationof 2nd mode growth

HFF on cone surface

HFF in stagnation point

Figure 11. Normalized HFF on cone surface for two different Reynolds numbers and corresponding stagnation pointHFF

tivity of free-stream disturbances and disturbances within the cone boundary-layer. In the frequency rangeof the second mode, factors of 20÷100 between the normalized fluctuation amplitudes on the surface andin the stagnation point are reached. It must be noted that the spectrum of the stagnation point probe inthis range is dominated by several peaks discussed in sec. III.A and their origin still remains to be verified.The rms-valus of the fluctuation spectra are given in Figure 11 to generally quantify the trend of this valueduring BL transition. It rises from from 42% to 71% on the cone surface, whereas the rms determined bythe stagnation-point probe is only 6.5%.

In order to investigate the possible influence of roughness created by the flat ALTP sensor module onBL transition, a study by means of artificial roughness placed upstream of the sensor array was carried out.The question that arises for the presented transition study is, whether the surface roughness created by thesensor modules is small enough not to affect transition. A criterion that is proposed to quantify a surfaceroughness in such a way is the Reynolds number Rek = ρkukk/μk based on the maximum roughness heightk (see review by Schneider16 and references therin). Here boundary-layer computations were carried out tocalculate specific Rek-values. It is stated that in general a roughness with Rek < 10÷ 25 is unlikely to affecttransition (unless there is a mechanism for amplifying weak streamwise vorticity). This criterion will beused as an indicator in combination with measured amplitude spectra with and without artificial roughnesselement.Contoured roughness elements with a diameter of 8 mm, simulating the ALTP sensor module, were extendedand retracted at several x-location upstream of the ALTP array. In the presented experiments, the maximumroughness height created by the most upstream ALTP sensor, when its streamwise diameter is aligned withthe cone surface, was k≈0.25 mm. Figure 12 shows several amplitude spectra of the most upstream ALTPwith the roughness elements in reference to the smooth cone spectra. The elements were extended by k≈0.25mm for increasing upstream positions (from x=225 to 175 mm) and k≈0.5 mm at the most downstreamposition x=175 mm. Thereby the ratio of roughness height k to boundary-layer thickness δ (taken from BL

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computations) and Rek was successively increased. In addition, the influence of a cavity of k≈ -0.25 mmwas investigated.The results show that all roughnesses with k≈ 0.25 mm and the cavity did not have a noticeable effect.The amplitude of the second mode varied within the repeatability of the reference cases for the smoothcone (hollow symbols). Only the roughness of k≈ 0.5 mm, corresponding to k/δ=0.37 at the most upstreamposition shows an explicit influence. The maximum amplitude of the second mode is increased by a factorof 6, a shift of the peak towards lower frequencies is visible and the first harmonic of the second mode isstrongly amplified. For this case, Rek ≈ 55 is beyond the interval that is postulated to have unlikely influenceon transition. All other experiments stay below or at the the lower limit of this interval (Rek < 10 ÷ 25 ),because Rek was always below 12 in all experiments. Therefore, this criterion seems to apply for the presentexperiments and the roughness created by the flat ALTP sensor module seems to be marginal and does notaffect the transition study on the present smooth cone experiments.

smooth conesmooth cone+0.25 225 +0.16 1.24 9.6+0.25 200 +0.17 1.24 10.4+0.25 175 +0.19 1.23 11.5+0.50 175 +0.37 1.23 54.8-0.25 175 -0.19 1.24 -

k [mm] x [mm] k/δ Rex [Mio.] Rek [Mio.]

f [kHz]

q’[W

/cm

2 ]

0 100 200 300 400 50010-3

10-2

10-1

100

Figure 12. HFF spectra for different roughness elements and cavity in reference to smooth cone spectra, measured atx = 295 mm

IV. Conclusion

The flow quality of the HLB was documented for different unit Reynolds numbers and different positionsin the test section. The spectral distributions of pitot-pressure fluctuations and fluctuations of heat flux inthe stagnation point of a blunt body, which correlate with total temperature fluctuations, were documentedin order to quantify the disturbance level of the facility in a frequency range up to the high kHz-range. Whilethe intensity of the pitot pressure fluctuations depends on the boundary layer conditions on the nozzle wall,i.e. they are unit Reynolds number dependent, the heat flux fluctuations depend on the convective flow inthe driver tube. All spectra show a typical decay of disturbances amplitudes vs. frequency. For the heat fluxfluctuations, dominant frequencies were detected but their origin is not unambiguously clarified and needsfurther systematic investigations.Hypersonic transition on a sharp cone at zero angle of attack was examined and the spatial amplification ratesof the second-mode instability could be calculated from spectra simultaneously measured by a streamwise

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array of fast-response heat flux gauges. A comparison of normalized fluctuation amplitudes on the surface ofthe cone and in the stagnation point showed amplification factors ranging from 20 to 100 near the frequencyrange of the second mode. For low frequencies, a factor of 10 was measured. Computational and theoreticalstudies still ongoing could help to interpret these results.In addition, the non-intrusive character of the streamwise sensor array was examined and confirmed for theactual experiments. The flat sensor modules represent small local roughness elements which are known toinfluence the transition scenario. But only artificial roughnesses much larger than the roughness typicallycreated by an ALTP sensor showed a significant effect on the amplitude spectra. This result is in goodagreement with the correlation based on roughness Reynolds number Rek, a common criterion used toestimate such a surface roughness influence.

Acknowledgments

This research was supported by the German Research Foundation (DFG) within the projects KA 1808/2-1and KN 490/2-1.

References

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