Experiments in Fluids

, Volume 50, Issue 2, pp 457–464

Non-intrusive generation of instability waves in a planar hypersonic boundary layer

Authors

    • Institute of Fluid Mechanics, TU Braunschweig
  • C. Kähler
    • Institute of Fluid Mechanics and AerodynamicsUniversität der Bundeswehr München
  • R. Radespiel
    • Institute of Fluid Mechanics, TU Braunschweig
  • T. Rödiger
    • Institute of Aerodynamics and Gas DynamicsUniversität Stuttgart
  • H. Knauss
    • Institute of Aerodynamics and Gas DynamicsUniversität Stuttgart
  • S. Wagner
    • Institute of Aerodynamics and Gas DynamicsUniversität Stuttgart
Research Article

DOI: 10.1007/s00348-010-0949-2

Cite this article as:
Heitmann, D., Kähler, C., Radespiel, R. et al. Exp Fluids (2011) 50: 457. doi:10.1007/s00348-010-0949-2

Abstract

The aim of this work is to show the possibility of non-intrusively exciting second-mode instability waves with arbitrary frequency and amplitude in a hypersonic, planar boundary layer, by means of optical methods. Surface heat flux sensors were used to measure natural and artificially excited instability waves on a flat plate at zero angle of attack. The measurements were made using a stream-wise array of flush-mounted high-frequency heat flux sensors. In addition, surface pressure sensors were applied and show the instability waves, as well. The possibility to generate such waves by locally heating the model surface is shown.

1 Introduction

The study of laminar-turbulent transition in hypersonic boundary layers is important, because of its dramatic effect on heat transfer, skin friction and separation. Despite several decades of research on the topic, the physics of the complete transition process is not understood well enough for prediction purposes. In case of quiet free stream flows, the transition scenario within a zero pressure gradient boundary layer (BL) is characterized by the following four stages: (1) receptivity, (2) linear amplification, (3) non-linear amplification and (4) breakdown to turbulence. For non-quiet free stream flows bypass transition may occur, but this is not critical here. Several instability modes are known.

Within a planar hypersonic BL, the second mode is expected to dominate the transition, according to linear stability theory, Mack (1984). The second-mode type instability waves appear sporadically (as isolated instances) in the time traces of the sensors as wave packets of several oscillations with frequencies in the high kHz-range, Stetson and Kimmel (1992), Kimmel and Poggie (1997), Poggie and Kimmel (1997). Toward completed transition, the amplitude increases and the wave packets spread out, i.e. the number of oscillations within the packet increases. For natural transition, the wave packets possess varying properties i.e. different initial amplitudes and frequencies. Hence the generation of artificial waves with repeatable properties is desirable for studying the behavior of these waves in detail. Due to the fact that the unstable frequencies are in the high kHz-range, a perturber cannot be realized mechanically.

Two kinds of perturbers are reported in the literature. In some references, artificial disturbances are generated inside the boundary layer using an electric glow discharge (see e.g. Kosinov et al. 1990; Ladoon and Schneider 1998; Kendall 1967). Further experiments were conducted at Princeton on a flat plate (Graziosi and Brown 2002; Brown and Graziosi 2000). In other references, a high-power laser is used for the disturbance generation in the free stream or on the model. For example, Glumac et al. (2005) or Salyer et al. (2006) described laser-generated hot spots and their evolution and Schmisseur et al. (2002) analyzed the response of a boundary layer of an elliptic cone to a small volume of heated gas that remains from a laser-generated plasma after some microseconds. Besides, laser disturbances were used for various kinds of flow control (see e.g. Elliott et al. 1998; Yan et al. 2002; Adelgren et al. 2003).

Although electric perturbers are reported more frequently in the literature on BL stability experiments, an optical system might offer some advantages. Glow dischargers might disturb the flow mechanically even when they are switched off and their location cannot be altered once they are installed. With an optical perturber the disturbance shape can be changed from a point to a line or even extended area simply by beam shaping optics and the location can be continuously adjusted without modifying the model. In addition, the amplitude can be altered over a large range, and the frequency is adjustable by simply setting the time delay between consecutive pulses (see Kähler 2005; Kähler and Dreyer 2004; Kähler and Scholz 2003 for details).

2 Experimental setup

2.1 Facility

The experiments were performed in the Hypersonic Ludwieg Tube Braunschweig (HLB), shown in Fig. 1. The HLB is a blow-down wind tunnel, which runs at a nominal Mach number of 6 for about 80 ms at conventional noise level. The possible unit Reynolds number range is (3–20) × 106/m, but for the stability experiments reported here only values up to 6.6 × 106 1/m were selected. In Table 1, the flow conditions of the experiments described here are summarized. The model temperature was not measured and is assumed to be Tw ≈ 300 K, giving a wall temperature ratio of Tw/T0 ≈ 0.63. The driver tube of the HLB is separated from the low pressure section, consisting of nozzle, test section, diffuser and a dump tank, by a fast-acting valve. The driver tube is heated along the first 3 m upstream of the valve. The heated section accommodates the amount of gas that is released during one run. The valve consists of a streamlined center body on the tube’s axis. The nozzle maintains an opening half angle of 3°, which results in slightly expanding flow in the test section with Mach numbers between 5.8 and 5.95 depending on the axial position and on the unit Reynolds number. The driver tube pressure is recorded with an accuracy of ±1%. The temperature in the driver tube is measured at two positions during the run. It must be noted that the measured temperature difference between the upper and lower measurement positions can be as high as 30 K due to temperature stratification. Hence, the measured value is not exactly the total temperature at the height of the model in the test section. Thus the determination of the unit Reynolds number is affected by uncertainties in total temperature, pressure and Mach number in the test section and the overall uncertainty is about ±2% in the relevant unit Reynolds number range according to Estorf (2008).
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Fig. 1

Cross-sectional view of the Hypersonic Ludwieg Tube Braunschweig (HLB)

Table 1

Table of flow conditions and estimated most unstable second-mode frequency (δ based on a reference distance along the model of 283 mm)

p0 (kPa)

T0 (K)

Re (×106 m−1)

0.9Ue/2δ (kHz)

394

467

3.4

88

502

466

4.3

99

613

475

5.2

108

706

480

5.8

115

802

481

6.6

123

730

480

6.1

117

444

478

3.7

92

396

476

3.3

87

499

482

4.1

97

2.2 Model

The model is a flat plate (630 × 200 mm2) made from steel. The leading edge is sharp and bevelled with an angle of 10°. Supersonic triangular edges (330 mm length, 70 mm width) are attached to the sides in the front part in order to minimize 3D effects.

2.3 Instrumentation

A preliminary test to measure the surface heating after a laser pulse was done with an Indigo Phoenix infrared camera. The CMOS InSb sensor is sensitive in the mid infrared range (wavelength of 3–5 μm). The integration time was set to 4 ms and the frame rate was 230 Hz.

Natural and artificial instability waves were measured with two different sensors. The use of two different measurement quantities provides confidence in the perturbation approach since an instability wave should be seen on different sensor types. First, an array consisting of 12 heat flux gauges was mounted 316 mm behind the sharp leading edge on the model centerline, yielding measurement positions from 283 to 349 mm with a spacing of 6 mm. The gauges are so called atomic-layer thermopile (ALTP) sensors. The working principle is based on the transverse Seebeck effect. These gauges have a time constant of approximately 1 μs. The output signal is directly proportional to the heat flux density at the wall. Details about the gauges and calibration methods are reported in Knauss et al. (2009) or Rödiger et al. (2008b).

Second, surface-mounted high-frequency pressure sensors (PCB M131A32) were used. Such sensors were already used in the past to measure second-mode waves see e.g. Rödiger et al. (2008a) or Estorf et al. (2008). The diameter of the active area is 3.18 mm. Power was supplied by an additional PCB instrument (M483A), which, at the same time, performed signal conditioning. The sensors have sensitivities of approximately 0.02 mV/Pa and a resolution of 7 Pa. For further details, the reader is referred to the manufacturer PCB Piezotronics. The sensors were placed at distances of 284, 300 and 316 mm from the leading edge on the centerline.

The heat flux and pressure data were sampled with a Spectrum M2i.4652 transient recorder. The sampling frequency was set to 3 MHz and the data were stored in 16 bit format. Time traces of 265 ms length were recorded, consisting of about 180 ms before/after and 80 ms of data during the tunnel run.

2.4 Perturber

A frequency-doubled Nd:YAG double-pulse laser (Quantel Brilliant) was used to generate the disturbances. The pulse length is approximately 4.2 ns at a wavelength of 532 nm. The maximum output energy is 150 mJ per pulse. When such a high-power laser pulse hits the model, the surface is locally heated and evaporated. Within this region, the laser light is absorbed and a plasma is generated. An approximately spherically propagating shock wave is formed, which attenuates to an acoustic wave within a few microseconds. After the end of the laser pulse, the plasma core relaxes and a region of hot gas remains. Accordingly, a laser perturbation at laser powers high enough to ignite a plasma includes a pressure disturbance and a disturbance from the heated gas and model (Kähler 2005). Whether a plasma is formed depends on the energy density, i.e. on the laser power and on the illuminated area. Both parameters were varied in the experiments. To simplify the disturbance for some of the experiments, the laser energy was reduced to approximately 25 mJ/pulse and the spot size was extended. With this setup, no plasma is formed and the perturbation consists only of a local heating of the model surface. As already mentioned above, experiments with heat flux and pressure sensors were done. These measurements were not done simultaneously and there was a marginal difference in the disturbance position. The position varied between 243 and 260 mm behind the leading edge.

A preliminary test was performed to measure the model surface heating according to Kähler and Scholz (2003). In Fig. 2, the thermal decay of the surface after heating with laser pulses is shown, which gives a measure of the disturbance repeatability. The energy stability was already previously measured and is 5–7%. But this was done at maximum pulse energy and the energy stability might be different at reduced laser power. The laser settings (pulse energy and spot size) in Fig. 2 match approximately the settings for the experiments with lowest laser power, where no plasma is generated. No temperature calibration was done and the temperature is given as gray scale value of the infrared camera. The average of 50 laser pulses (solid line) and single measurements (circle) are given. The model is abruptly heated when hit by the laser. This heating is followed by an exponential decay of the temperature. The deviation of the single measurements to the average is in the order of 3 counts, which is less than 1 K.
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Fig. 2

Thermal decay of the model surface after heating with a laser-pulse, solid line average, circle single measurement

3 Results

3.1 Natural transition

At first, some properties of the natural transition are given for comparison. Therefore both, heat flux and pressure measurements were conducted. For more details, the reader is referred to Rödiger et al. (2008a). In Fig. 3, the amplitudes of the Fourier modes caused by the disturbances measured at a distance of 283 mm from the leading edge, for a variation of unit Reynolds number, are shown. For these curves, time traces of approximately 50 ms were divided into segments of 1,500 points. Each segment was multiplied with a normalized Blackman window and Fourier transformed. The average of these windows was taken and a signal prior to the tunnel run was subtracted, to reduce electric noise. The chosen window size gives a frequency resolution of 2 kHz.
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Fig. 3

Disturbance spectra (heat flux) on flat plate at X = 283 mm for different unit Reynolds numbers

Experiments studying planar BLs in the literature (e.g. Stetson et al. 1991; Rödiger et al. 2008a and references therein) showed the presence of a low-frequency disturbance beside the second mode. The origin of this low-frequency disturbance is unclear. However, the expected second mode appears as well, as shown in Fig. 3. At low Reynolds number (Re = 3.4 × 106 1/m), a small peak at 75 kHz is visible. With increasing Re, the peak moves to higher frequencies and the amplitude increases. At Re = 6.6 × 106 1/m disturbances above and below the second-mode peak appear while the second-mode amplitude decreases. The frequency shift can be explained with the tuning of the instability wavelength to the boundary layer thickness (see e.g. Stetson and Kimmel 1992). The wavelength of a second-mode wave is approximately twice the boundary layer thickness δ and the propagation velocity is slightly below the BL edge velocity Ue. Therefore, the most unstable frequency can be approximated with f = 0.9Ue/2δ. The estimates for these frequencies are given in Table 1. The BL thickness δ was calculated from similarity profiles according to Van Driest (1952). The agreement between estimated and measured frequency is quite good, especially for the cases Re = [4.3–5.8] × 106 m−1.

The second mode appears quite strong compared to other flat plate experiments in the literature (e.g. Stetson et al. 1991). In other investigations, the second mode was not detectable at all. For example, the experiments of Wendt et al. (1995) showed only the existence of first-mode waves. The reason for that is not clear, but there are three points that might have caused the differences. (1) The measurements were performed in different facilities with different noise environments. (2) Different measurement techniques were applied, i.e. in the present case, heat flux sensors were used instead of previously used hot wires which should give a measure of the mass flux. (3) Because of the different techniques the measurement position was different, as well. While Stetson measured near the boundary layer edge the measurement position in the present experiments was at the wall.

In the time traces, the frequency content is indicated by wave packets, which grow while they convect downstream. One of these wave packets is depicted in Fig. 4. For this and the following figures showing time traces, the sensor signal was band-pass filtered between 50 and 250 kHz. The amplitude of a single wave is much larger than the value in the amplitude spectra (Fig. 3), because the spectra represent the means of many windows with only some of them containing waves. At a distance of 283 mm from the leading edge, a wave consisting of three oscillations with an amplitude of about 1,000 W/m2 passes the sensor at t = 0. A few microseconds later, it passes the sensor at X = 295 mm and the amplitude increases by a factor of more than five. In addition, more oscillations (5–6 periods) are now detectable. Between X = 295 and 313 mm, the amplitude increases further. The propagation speed of the wave is about 800 m/s or 88% of the boundary layer edge velocity. This propagation velocity is in good agreement with data reported in the literature (see e.g. Stetson and Kimmel 1992; Poggie and Kimmel 1997). There the measurements were performed with hot wires at a wall distance where maximum RMS output voltage was recorded. This distance was close to the boundary layer edge and hence the propagation speed is close to the edge velocity.
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Fig. 4

Time traces of a natural wave packet at three positions for Re = 3.7 Mio./m using heat flux sensors

Disturbance spectra and time traces of waves measured with surface pressure sensors look similar to the results in Figs. 3 and 4. In Fig. 5, amplitude spectra for two subsequent positions at a fixed Reynolds number are shown. As in Fig. 3, a peak related to the second mode is at approximately 100 kHz. Further, the Reynolds number dependence of amplitude and frequency is visible. The time traces of the surface pressure are qualitatively very similar to the surface heat flux shown in Fig. 4 and are therefore not given here.
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Fig. 5

Disturbance spectra (pressure) on flat plate at Re = 6.05 × 106 1/m for two measurement positions

3.2 Artificially excited waves

For artificially excited waves, both heat flux and pressure measurements are given and three different disturbance modes are treated here. At first, the boundary layer response to a single point-shaped disturbance is shown. Later, the disturbance shape is changed to a line and than two laser pulses are used in an attempt to impose a certain frequency on the wave.

In Fig. 6, time traces of a pressure sensor 40 mm downstream of a point-shaped disturbance (\(\varnothing 2\) mm) are given. The disturbance position was at a distance of X = 260 mm from the leading edge. The disturbance consisted of a single laser pulse at t = 0 and E ≈ 110 mJ. At such high laser power, a plasma is generated and the associated shock wave reaches the sensor 30 μs later. A small wave consisting of two oscillations is generated behind the shock wave.
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Fig. 6

Time traces of artificial wave at X = 300 mm for Re = 4.1 Mio./m using pressure sensors, distance to laser disturbance ΔX = 40 mm, laser spot \(\varnothing 2\) mm and E ≈ 110 mJ, solid line mean, circle single measurement

The solid line represents the band-pass-filtered mean of five tunnel runs and the symbols show one of the underlying single runs. The phase of the wave is in good agreement, whereas the amplitude shows some slight deviations. The frequency content of the wave packet is in the range of the second mode, as can be deduced from the Δt ≈ 10 μs between consecutive crests which corresponds to a frequency of 100 kHz. The generation of such a wave is repeatable within certain limitations. In total, ten tunnel runs were done at the conditions in Fig. 6 and there are two noteworthy influencing factors, why the repeatability is limited to about 50%. First, due to the noisy flow, most of the time natural waves are present and interact with the artificially excited wave. Tunnel runs, in which natural waves could be seen in the time interval, where the disturbance was expected, were excluded from the averaging. Second, although the thermal surface disturbances generation in Fig. 2 appears well repeatable, it has to be noted, that the repeatability for the first laser pulses within a sequence is not as good. Therefore, one tunnel run was excluded, because the disturbance looked somewhat different. In total, half of the tunnel runs were excluded mainly due to the presence of natural waves.

The amplitude of the wave in Fig. 6 is very large. In addition, it is unclear whether the thermal disturbance or the pressure disturbances caused the wave generation. Therefore, the laser power was reduced until no plasma was generated anymore. In Fig. 7, the dependence of the resulting wave on the laser energy is shown. In both cases, no plasma was formed. Time traces of a heat flux sensor 40 mm downstream of the disturbance position are given for two different laser power settings. The laser fires at t = 0 and a wave passes the sensor 60 μs later. For higher laser power, the resulting wave has a larger extension in streamwise direction. The wave amplitude does not change considerably.
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Fig. 7

Time traces of artificial wave at X = 283 mm for Re = 3.3 Mio./m using heat flux sensors, distance to laser disturbance ΔX = 40 mm, laser spot \(\varnothing 1\) mm

The perturbation generated by such small pulse energies with this relatively large diameter consists only of a thermal disturbance. Since no plasma ignites, there is no shock wave propagating from the disturbance position. It seems that the locally heated model results in a local and abrupt heating of the gas when it convects over the disturbance position. The time, during which this heating takes place, is only very short as indicated by the initial slope of the cooling curve shown in Fig. 2. The boundary layer is locally influenced by the heating and this disturbance contains stable and unstable modes. While the stable modes are damped, the unstable modes are amplified and form the wave.

A possible influence of the irradiated area was examined by focussing the laser to a line and this is shown in Fig. 8. The light sheet (40 × 0.5 mm2) was perpendicular to the flow direction and the power was about the same as in Fig. 6. But since the area for the line-shaped disturbance is larger, the energy density and hence the surface heating is smaller. Again, the laser fires at t = 0 and the average of five tunnel runs and a single tunnel run are shown. The boundary layer response to the line-shaped disturbance is qualitatively the same as for the point-shaped disturbance.
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Fig. 8

Time traces of artificial wave at X = 300 mm for Re = 4.1 Mio./m using pressure sensors, distance to laser disturbance ΔX = 40 mm, irradiated area (40 × 0.5 mm2) and E≈ 110 mJ, solid line mean, circle single measurement

The third parameter that is examined here is the usage of two pulses with a time delay between. This might offer the possibility to impose a certain frequency at the inverse of the pulse spacing. Figure 9 shows the time traces of a heat flux sensor 40 mm downstream of the disturbance position. In this case, the laser was focussed to a line perpendicular to the flow direction and the pulse energy was E ≈ 75 mJ. The first pulse is fired at t = 0 and visible from an electric disturbance. The ALTP gauges are more sensitive to such disturbances than the pressure sensors. In the upper part, the time between the pulses was set to 13.33 μs. About 50 μs after the first laser fires, the wave passes the sensor and the set time distance can be found in the time trace. For the lower part of the figure, the set time distance was 10 μs and this can be found in the time trace, as well.
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Fig. 9

Heat flux time traces (X = 283 mm, ΔX = 40 mm) after disturbance with two laser pulses with different Δt between (40 × 0.5 mm2, E ≈ 75 mJ)

So far only single-point measurements were shown. The evolution of an artificially excited wave is given in Fig. 10. Here, the surface heat flux was measured. In this case, two laser pulses were fired with a Δt = 10 μs between them. This Δt corresponds to a frequency of 100 kHz and it was chosen, because natural waves are most unstable near this frequency, see Fig. 3.
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Fig. 10

Time traces of an artificial wave packet at three positions for Re = 3.7 Mio./m; X means distance from leading edge, ΔX means distance from disturbance position

The first pulse is at t = 0 and again visible from an electric disturbance perceived by all sensors. At the first measurement position, 40 mm downstream of the perturbation location, a small wave is visible. In the beginning, this wave seems to contain several different wave numbers, as can be suspected from the deformation of the wave in the beginning (t≈ 30–50 μs). Later, a frequency of approximately 100 kHz dominates the wave and the wave has grown by a factor of about five. A natural wave appears also in the time traces of the middle and rear sensors at t = 180–200 μs, but this is not related to the perturbation. In Fig. 11, the amplitude disturbance spectra of the wave in Fig. 10 are given. Therefore, short time segments (t = 20–150 μs) were multiplied with a normalized Blackman window and Fourier transformed. Since there was no averaging, the signal was quite noisy and a moving average consisting of five points was taken. With the short time trace used the frequency resolution is 7.7 kHz.
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Fig. 11

Disturbance spectra of an artificial wave packet at three positions for Re = 3.7 Mio./m; X means distance from leading edge, ΔX means distance from disturbance position

The amplification and the frequency tuning with changing running length can be seen and the unstable frequencies are in the range of the second mode. The amplification rate −αi between X = 283 and 295 mm is in the range of 150 m−1 and this is much larger than computational predictions of linear stability theory, indicating transient growth. Between X = 295–313 mm −αi is in the range of 50 and this is only little larger than LST results (see Rödiger et al. 2008a).

4 Summary

Instabilities within a hypersonic planar boundary layer were measured. The unstable frequencies agree quite well with estimates based on relations from the literature. Further, the possibility to excite second-mode instabilities by locally heating the model surface with laser pulses was demonstrated. The excited waves were measured in terms of two different physical quantities and they look quite similar to naturally occurring waves. The present study aimed to show the possibility for the excitation of waves by an optical perturber. Hence, the laser energy was set to relatively large levels to obtain better repeatability. However, comparisons of the experimental data with the results of linear stability computations indicate that the initial wave amplitudes might have been too large. Future experiments should therefore be performed with smaller excitation energies.

Acknowledgments

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

Copyright information

© Springer-Verlag 2010