FREE TRANSITION ON A SLENDER CONE IN A QUIET AND A CONVENTIONAL WIND TUNNEL AND THE EFFECT OF ULTRASONICALLY ABSORPTIVE MATERIALS

Transition from laminar to turbulent hypersonic boundary layers is the topic of several research projects world-wide. Most experimental work is done in conventional wind tunnels, although their free stream turbulence does not match free §ight conditions and has a signi¦cant in§uence onto the transition process. Experiments performed with the same 3 degree half angle cone in a conventional and a quiet wind tunnel at Mach 6 justify this approach. The formation, ampli¦cation, and decay of the second (Mack) modes is compared based on high-frequency pressure measurements. In addition, damping of these modes with ultrasonically absorptive surfaces was tested.


INTRODUCTION
The transition from a laminar to a turbulent boundary layer is accompanied by an increase of the heat §ux and drag.Therefore, it is essential for the design of hypersonic vehicles to predict the transition location correctly.In addition, it is often desirable to delay the transition as long as possible.In nonlifting hypersonic §ows over smooth surfaces, the transition is most likely provoked by the ¦rst and second mode instabilities.As the ¦rst mode (TollmienSchlichting waves) can be damped by cooled structures, the second mode (Mack mode) becomes dominant.The formation and ampli¦cation of the second (Mack) mode is the topic of several research projects.Most of the experiments are performed in classical wind tunnels although the free stream §uctuations have a signi¦cant e¨ect onto the transition process.The disturbance level in a quiet wind tunnel is one or two orders of magnitude lower and, therefore, much closer to the conditions at real §ight.But there are just a few quiet wind tunnels and their operating envelope is limited.A direct comparison of experiments in a quiet and a conventional wind tunnel is important to identify the drawbacks and opportunities of conventional wind tunnels for hypersonic transition research.
The experiments presented in this paper were performed in the Boeing/AFOSR Mach-6 Quiet Tunnel (BAM6QT) at Purdue University and in the hypersonic wind tunnel (H2K) of the German Aerospace Center (DLR) in  Cologne.To improve comparability, the same model, sensors, and data acquisition system were used.
There are numerous attempts for passive or active damping of these trapped acoustic waves.Rasheed et al. [1] demonstrated a damping of the second (Mack) modes and a delay of the transition on a 5 degree half cone with a regular porous surface at Mach 5. Fedorov et al. [2] and Wagner et al. [3] veri¦ed the damping of these acoustic waves with a 7 degree half cone and a porous coating of random microstructures at Mach 6.For the transition experiments presented here, a 3 degree half angle cone with either a plain surface, regular holes, or a random porous surface was tested at Mach 6.
The used model (Figs. 1 and 2) is equipped with PCB sensors for the detection of pressure §uctuations at high frequencies as well as Kulite sensors for those at intermediate and low frequencies.The main model parts are made of polyether ether ketone (PEEK) to enable simultaneous measurements of the transition position with infrared cameras for the H2K experiments.For the BAM6QT experiments, the rear segment was replaced with an aluminium segment to use temperature sensitive paint (TSP).

Model
The basic model shape is a circular cone with 3 degree half angle.The model consists of three exchangeable segments: the apex, the middle segment, and the rear segment, and is supported by a central steel shaft (see Fig. 1).A sharp steel apex with a nose radius below 0.15 mm was used for all experiments in this paper.Three di¨erent middle segments were in use.Two made of PEEK allow quantitative infrared thermography in H2K: the ¦rst with a plain surface and the second with a generic porous surface formed by regular uniform blind holes.The holes are 80 µm in diameter, at least 1000 µm in depth, and placed every 200 µm, thus the porosity is 12.6%.A close-up is shown in Fig. 2a.The choice of the hole dimensions originates from the simulations [4,5] with NOLOT and technical feasibility.The Fraunhofer Institute for Laser Technology (ILT) in Aachen performed the manufacturing of these holes with the help of laser drilling [6] using a pulsed INNOSLAB laser.In circumferential direction, one third (120 • ) of the surface is perforated.The perforated area starts at a radius of 15.5 mm and ends at a radius of 39.5 mm; thus, the porous area has a length of 456 mm and contains about 660 000 holes.The third middle segment is made of a C/C material with a random porosity (see Fig. 2b) manufactured by the DLR Institute of Structures and Design in Stuttgart.The typical diameter of the pores is 10 to 40 µm and the porosity is 12.1%.The rear segment used in H2K is made of PEEK and has a base radius of 90 mm.Due to the smaller core of uniform §ow in the BAM6QT, two shorter rear segments with base radius of 45 and 50 mm were used.They are made of aluminum, slightly undersized to allow for the application of TSP, since infrared thermography is not possible in the BAM6QT.

Quiet Wind Tunnel BAM6QT
The Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) is a Ludwieg tube with a long driver tube and converging-diverging nozzle for Mach 6.A schematic of the tunnel is shown in Fig. 3. Several features ensure a laminar boundary layer on the nozzle walls.This includes boundary layer suction upstream of the throat, slowly increasing diameter in the divergent section of the nozzle, polished nozzle walls, and the position of the burst diaphragms downstream of the test section.With this, the turbulence level of the free §ow in ¤quiet¥ mode is of the order of 0.05%.If the bleed lip for the boundary layer suction is closed, the tunnel operates in ¤noisy¥ mode with a turbulence level of the  order of 3%.The air in the driver tube is pressurized up to 2 MPa and electrically heated up to 430 K.The length of the driver tube ensures stable §ow conditions for about 100 ms and the stepwise blowdown measurements with several Reynolds numbers in the same run.Figure 4a shows the test section with the model.The in §ow conditions of the experiments in BAM6QT are listed in Table 1.

Conventional Wind Tunnel H2K
The hypersonic wind tunnel Cologne (H2K) is a classical blowdown wind tunnel with a free jet test section and a test time of 30 s.A schematic of the tunnel is shown in Fig. 5.For the experiments, a Mach 6 contoured nozzle with an exit diameter of 600 mm was used.The test gas air is heated with resistance heaters.
Figure 4b shows the test section with the model.For further information about the H2K, see [8].The in §ow conditions of the experiments in H2K are listed in Table 1.

Data Acquisition
For the experiments, the same data acquisition system was used and the same sensors as far as possible.In H2K, the surface temperature on the PEEK segments is captured via two infrared cameras.The top view is captured with an AGEMA THV570 at a sample rate of 50 Hz and a resolution of 320 × 240 pixel.The side view is captured with a FLIR SC3000 at 60 Hz and a resolution of 320 × 240 pixel.In both facilities, the model is at room temperature (≈ 295 K) before the test.Since the sensor data used in this paper were captured within the ¦rst second after wind tunnel start in BAM6QT and within the ¦rst two seconds after wind tunnel start in H2K, the increase of the wall temperature is a few kelvin in laminar regions and not more than 10 K in turbulent regions.

Data Processing
The averaged frequency spectra, shown in this paper, base on 500 000 data points at 0.1 s stable §ow conditions divided into 39 blocks with 25 000 samples each.Adjacent blocks overlap by 50%.All values are normalized with static pressure of the in §ow and then each block is multiplied with the Hann function.For each block, the power spectral density is computed.The arithmetic mean of all spectra is the ¦nal result.This procedure is also known as Welch£s method.
Hence, the frequency spectra show root mean square values scaled with the frequency.
To resolve single turbulent spots and wave packages, the PCB data are also processed using a complex Morlet wavelet analysis [9,10].The wavelet function used here is a sine function limited in time by a Gaussian distribution: The wavelet transforms performed in this paper are based on 5 000 samples and use 2 500 scales of the wavelet with the same maximum amplitude of frequency response.Therefore, the time resolution is 2 µs and the frequency resolution is 1 kHz.The raw data of the infrared cameras are transferred to heat §uxes and Stanton numbers using the in-house tool VisualHeatFlow (for the algorithm, see [11]).The recovery factor for the postprocessing of the infrared images is always set to the value of a laminar boundary layer √ Pr = √ 0.73.The used coordinate system has its origin at the tip of a perfect sharp cone with the x-axis pointing in §ow direction and the z-axis to the top of the test section.

Model Alignment
The model support in H2K allows adjustment of the pitch and yaw angles.A correct alignment results in a symmetric transition region on the cone surface.The two infrared cameras with top and side view allow the correction of the yaw and pitch angle.Figure 6 shows the alignment procedure in H2K.
As there is no rotatable model support in the BAM6QT, the sting was designed to allow small corrections of the yaw and the pitch angles.Since infrared thermography is not available and the TSP is only available on one side, the signal of the PCB sensors was used to check the alignment.If 4 PCBs around the circumference at the same x position measure the same amplitude of the second (Mack) mode, the model is correctly aligned.Figure 7 shows the alignment procedure in BAM6QT.

RESULTS
For all three in §ow noise levels ¡ BAM6QT in ¤noisy¥ mode, H2K, and BAM6QT in ¤quiet¥ mode, the second (Mack) modes were observed on the cone with plain surface.Figures 810 show the plots of the power spectral density computed from the PCB data in di¨erent runs.Good to see is the formation, ampli¦cation, and decay of the second (Mack) modes.It is important to note that the decay of the modes and, hence, a transition to a turbulent boundary layer was observed in quiet §ow, too, even though usually a compression cone is used to obtain free transition in quiet §ow in BAM6QT.In BAM6QT in noisy mode at Re u,∞ = 2.4 • 10 6 m −1 , the second (Mack) mode is detected at a frequency of about 70 kHz.It disappears between the sensors at s = 900 and 945 mm (see Fig. 9c) which results in a Reynolds number of about 2.2 • 10 6 for the completion of the transition process.In H2K, at Re u,∞ = 3.2 • 10 6 m −1 , the second (Mack) mode is detected at a frequency of about 100 kHz.The transition process is completed between the sensors at s = 945 and 1135 mm (see Fig. 8a) which results in a Reynolds number of about 3.2 • 10 6 m −1 .At Re u,∞ = 4.1 • 10 6 m −1 , a sensor at s = 765 mm also measures the ¦rst and second harmonic of the second (Mack) mode (see Fig. 8b).In the BAM6QT in quiet mode at Re u,∞ = 11.5 • 10 6 m −1 , the second (Mack) mode is detected at a frequency of about 140 kHz.The transition process is almost completed at the sensor at s = 945 mm (see Fig. 10d ) which results in a Reynolds number of about 11.0 • 10 6 m −1 .The sensors at s = 810 and 855 mm also measure the ¦rst harmonic of the second (Mack) mode.Besides the shift to lower Reynolds numbers with increasing turbulent intensity of the in §ow, there is no principal di¨erence in the transition process observed.Also, the maximum of the normalized amplitude of the second (Mack) mode is of the same order of magnitude.This supports the attempt of Marineau et al. [12] of an amplitudebased method to account for the e¨ect of tunnel noise on the second (Mack) mode transition.This is supported by the wavelet plots in Figs.11 to 13. Figure 11 shows the wavelet analysis of data from H2K at Re u,∞ = 4.1 • 10 6 m −1 .The corresponding spectra can be found in Fig. 8b.At s = 341.2mm, the boundary layer is still laminar and the wavelet plot of the sensor data reveals no interesting features (Fig. 11a).At s = 548.0mm, the ¦rst compact packages of the second (Mack) modes occur that indicate a transitional boundary layer (Fig. 11b).They are limited in time and frequency.They increase in amplitude and number until s = 764.8mm (Fig. 11c).At s = 945.1 mm, the compact packages are destroyed   and spread in time and frequency (Fig. 11d ).There are no distinguishable packages at s = 1135.3mm but a vesicular structure covering the complete time span and a broad frequency band ¡ the boundary layer is fully turbulent (Fig. 11e).This is consistent with the measurements of free transition on a §at panel at 0 degree angle of attack as shown in [13].
The compact packages and their decay are also detected in BAM6QT at Re u,∞ = 11.5 • 10 6 m −1 as shown in Fig. 12.But at the last sensor, there are still distinguishable packages.This indicates, that the transition process is not fully completed.In the wavelet analysis of data at Re u,∞ = 9.5 • 10 6 m −1 , the same packages are visible on di¨erent sensors (see Fig. 13).This allows an estimation of the travelling speed of these package to 900 m/s which is close to the computed edge velocity of 850 m/s.
The comparison of the transition process with ultrasonically absorptive materials shows no damping of the second (Mack) mode or transition delay, neither in noisy nor in quiet §ow.  a small di¨erence in the amplitudes on the di¨erent materials, but the second (Mack) mode on the regular holes decay earlier than on the other materials, which even indicates an earlier transition there.The second (Mack) mode on the random pores decays just a little earlier than on the plain surface.This is consistent with the results of the infrared thermography made in H2K that show a slight shift of the transition region (indicated by a raise of the Stanton number) on the regular holes upstream (Fig. 16).
Figures 17 and 18 show the results from BAM6QT at Re u,∞ = 9.5 • 10 6 and 11.5 • 10 6 m −1 in quiet §ow.At Re u,∞ = 9.5 • 1− 6 m −1 , all sensors on the rear part detect strong second (Mack) modes (see Fig. 17).All ¦gures there show an ampli¦cation of the second (Mack) mode and a shift to lower frequencies on the regular holes and on the random pores compared to the plain surface.At Re u,∞ = 11.5 • 10 6 m −1 , the decay of the second (Mack) mode on the rear segment indicates the end of the transition region (see Fig. 18).The ¦gures there show an earlier decay of the second (Mack) mode and a shift to lower frequencies on the regular holes compared to the plain surface.With the random pores, the amplitudes are little higher at the ¦rst sensors compared to the plain surface.And the decay of the second (Mack) mode is a little faster on the last sensors.

SUMMARY
The experiments with the same sharp slender cone and the same data acquisition system carried out in the quiet wind tunnel BAM6QT and the conventional wind tunnel H2K at similar conditions at Mach 6 allow direct comparison of the laminarturbulent transition of a hypersonic boundary layer.Due to the small half angle of 3 • and the large model length, the ampli¦cation and breakdown of  the second (Mack) modes could be observed for noisy as well as for quiet conditions.While there are evident di¨erences in the transition locations between quiet and noisy conditions, the transition process and mechanism seem to be similar.
To test the damping e¨ect of porous surfaces, two alternative sections were used, one with regular holes and the other with random pores.The experiments performed in the BAM6QT under noisy and quiet conditions and in H2K provided similar results.Although the design of the holes and pores was based on numerical simulations, neither a signi¦cant damping of the second (Mack) mode nor a delay of the transition process occurred.On the contrary, the results indicate an ampli¦cation of the second (Mack) mode and an earlier transition, especially on the regular holes.The reason for this discrepancy is not yet known.A possible explanation are the lower frequencies of the second (Mack) mode on a 3 degree cone compared to a 5 degree cone used by Rasheed et al. [1] or to 7 degree cones used by Fedorov et al. [2] and Wagner et al. [3].Another reason could be the sensitivity of the damping to the position and length of the porous surfaces as found by Lukashevich et al. [14].

Figure 1
Figure 1 Drawing of the model with segments and marked sensor positions

Figure 2
Figure 2 Details of the ultrasonically absorptive surfaces: (a) PEEK surface with regular holes; and (b) C/C surface with random pores

Figure 6 Figure 7
Figure 6 Model alignment in H2K: top view infrared images of the cone with ceramic middle and PEEK rear segment: (a) model with 0.08 degree yaw angle; and (b) model correctly aligned

Table 1
Flow conditions for the testsWind tunnelMa T0, K p0, kPa T∞, K p∞, Pa Reu,∞, 10 6 m −1 The model is equipped with 8 to 12 PCB 132A31 sensors with a 350-kilopascal range and a resonant frequency above 1 MHz.They are connected to signal conditioners PCB 482C05 and their output signals are measured with Adlink PXI-9816D/512 digitizers, which enable a 16-bit resolution and a sample rate of 5 MHz.Three to ¦ve of the PCB sensors are placed on a generatrix numbered according to Fig.1with the exact positions given in Table2.At the positions 1, 3, 5, C, and E, there are 4 PCB sensors around the circumference.For the H2K experiments, the model is equipped with 4 Kulite XCQ-080 B-screen sensors with a 35-kilopascal range and a natural frequency of 150 kHz for static and low frequency surface pressure measurements.They are connected to a NI PXIe-4331 bridge module, which enables a 24-bit resolution and a sample rate of 100 kHz.For the BAM6QT experiments, they were replaced by two full scale stopped XCQ-062 A-screen sensors with a 100-kilopascal range.

Table 2
Model dimensions and sensor positions given by the local model radius r as well as the x-coordinate and the path length s measured from the nose tip