Non-intrusive generation of instability waves in a planar hypersonic boundary layer
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- Heitmann, D., Kähler, C., Radespiel, R. et al. Exp Fluids (2011) 50: 457. doi:10.1007/s00348-010-0949-2
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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.
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
Table of flow conditions and estimated most unstable second-mode frequency (δ based on a reference distance along the model of 283 mm)
Re∞ (×106 m−1)
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.
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.
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.
3.1 Natural transition
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.
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.
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 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.
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).
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.
This research was supported by the German Research Foundation (DFG) within the projects KA 1808/2-1 and KN 490/2-1.