Experimental investigation of the instantaneous spatial flow organization
of high-speed turbulent boundary layers
R.A. Humble, G.E. Elsinga, F. Scarano, B.W. van Oudheusden
Delft University of Technology, Aerospace Engineering Department, Delft, The Netherlands
Abstract:
Tomographic particle image velocimetry is applied to characterize the three-dimensional structure of turbulent boundary layers under compressible flow conditions. The instantaneous 3D flow organization of a turbulent boundary layer, as well as its interaction with an incident shock wave is investigated. Large-scale coherent motions within the boundary layer are observed, in the form of streamwise-elongated regions of relatively low- and high-speed flow, similar to those found within subsonic and other supersonic boundary layers. Vortical structures are shown to be associated with the low-speed regions, in a way that can be explained by the hairpin vortex packet model of incompressible boundary layers. In the shock interaction case, the instantaneous reflected shock wave pattern appears to conform to the low- and high-speed regions as they enter the interaction, consistent with previous observations in compression ramp interactions.
Introduction
The investigation of compressible turbulent flows is of significant importance for high-speed aeronautical vehicle applications but provides special challenges to the experimentalist. Due to the typically high Reynolds number of such flows, a large range of spatial and temporal scales is encountered, and the high convective velocities ensure that structures pass at very high-frequency in the Eulerian observation frame of stationary measurement probes. This places high demands on diagnostic techniques, such as hot-wire anemometry for example. In addition, the high-speed wind tunnel environment often places further limitations on measurement capabilities in comparison to the low-speed flow regime, in view of the restricted optical access and limited measurement times.
Understanding the structure of turbulence has traditionally been progressing gradually through a combined use of quantitative probe measurements (LDA and HWA) in combination with high-speed qualitative flow visualization. The application of particle image velocimetry (PIV) has introduced the possibility of capturing the instantaneous spatial flow organization in a quantitative manner, which has been extremely helpful in further characterizing the large-scale structure of turbulent flows in particular. Planar PIV (2C or 3C) allows the measurement of the instantaneous velocity field in a planar cross-section of the flow, but the inability to make instantaneous volumetric measurements often leads to ambiguities in the interpretation of the data, which necessitates various assumptions to be made in order to link these reduced-dimensional representations to the 3D structure of the flow organization. The present communication discusses the recent introduction of using tomographic-PIV (Elsinga et al. 2006) as a means for investigating the instantaneous 3D spatial flow organization of high-speed turbulent boundary layers.
Experimental arrangement
Experiments were performed in the blow-down transonic-supersonic wind tunnel (TST-27) of the High-Speed Aerodynamics Laboratories at Delft University of Technology. The tunnel was operated at a nominal freestream Mach number M∞=2.1 (freestream velocity U∞=503 m s-1) in a test section of dimensions 255 mm×280 mm. The boundary layer developing along the side-wall was chosen as the test boundary layer, which on entering the test section was δ=20 mm thick. The Reynolds number based on the momentum thickness, Reθ=U∞θ/v∞=3.96×104 (where v∞ is the kinematic viscosity in the freestream). Further details may be found in Elsinga et al. (2007). For the interaction experiment, a 70 mm chord shock generator imposing a deflection angle of 10º was placed in the freestream flow to generate the incident shock wave. The generator was mounted vertically in the centre of the test section on an 80 cm long sting and spanned approximately 65% of the test section height. Further details may be found in Humble et al. (2007).
The flow was seeded with 170 nm TiO2 particles, and illuminated by a Spectra-Physics 400mJ double pulse Nd:Yag laser. Four LaVision Imager Pro X (2048×2048 pixels) CCD cameras imaged the flow in streamwise (x), wall-normal (y) and spanwise direction (z) over a volume of approximately
70×8×35 mm3 (3.5δ×0.4δ×1.8δ) with an average resolution of 23 pixels/mm. Reconstructed volume dimensions were discretized at 203 voxels per mm3. The time separation between subsequent exposures was set at 2 μs, allowing a maximum particle displacement of 20 voxels. The camera system was calibrated by imaging a target plate at various depth positions within the volume. The relationship between physical and image coordinates was described by a 3rd order polynomial fit. Linear interpolation was used to find the corresponding image coordinates at intermediate depth positions. Self-calibration (see Wieneke 2007) was used to decrease the triangulation disparity to below 0.2 pixels. The intensity distribution in the volume was reconstructed from the recorded images using the MART algorithm (Elsinga et al. 2006). In the cross-correlation analysis of the 3D reconstructed objects the interrogation box size was progressively decreased to 403 voxels per mm3. A 75% overlap factor was applied, returning a vector spacing of 0.5 mm in each direction, resulting in an overall measurement grid counting approximately 140×15×80 vectors (vector grid spacing ca. 0.5 mm).
Figure 1: Experimental arrangement.
Results: Turbulent boundary layer
Figure 2 presents a typical example of the returned instantaneous flow field. Vortical motion (green) is visualized using the Q-criterion (see Hunt et al. 1988), and zones of low velocity (blue) are indicated by the isosurface u/U∞=0.8. A contour plot of the instantaneous streamwise velocity is also shown for comparison. The low-speed zones are several boundary layer thicknesses long, often extending beyond the measurement volume. Ganapathisubramani et al. (2007) report lengths up to 40δ at y/δ = 0.2 in their supersonic boundary layer, based on high repetition rate PIV measurements and using Taylor’s hypothesis. Long low-speed zones have also been found in incompressible turbulent boundary layers using a single hot-film (Kim & Adrian 1999) and a spanwise array of hotwires (Hutchins & Marusic 2007). The width of the low speed zones observed in the present experiments varies between 0.25δ and 0.4δ, consistent with the observations of Ganapathisubramani et al. (2006) and Tomkins & Adrian (2003) for example.
Figure 2: Results of tomographic PIV investigation of a turbulent boundary layer. Left: instantaneous vortex distribution using Q-criterion (green) and low speed zones (blue); Right: contour plot of the instantaneous u-component of velocity.
Plots of the complete measurement volume, such as in figure 2, reveal that most vortical structures are found near the low speed zones. A portion of figure 2 (left) is enlarged and shown in figure 3 (left). Around the low speed zone a series of streamwise aligned hairpin (or arch) vortices are
observed, which can be considered a hairpin packet (Adrian et al. 2000). The streamwise spacing of the vortices inside this packet is approximately 0.2δ. Figure 3 (right) presents the corresponding velocity vector field after subtraction of a convective velocity. The velocity distribution in the x–y plane (top diagram) shows swirling motion around the heads of the individual hairpins. For clarity, the circles indicate the location of the vortices. It is also seen that the vortex heads convect with slightly different velocities, what may result in the interaction or merging of the vortices at a later stage. Furthermore, the vortices are of approximately the same size and do not appear to be aligned along a 12 to 20 degrees slope with the wall, as reported by Head & Bandyopadhyay (1981) and Adrian et al. (2000). Near the top of the volume at y/δ = 0.45 the velocity direction and magnitude is very irregular, which may indicate the presence of (vortical) flow structures just above this packet. Finally, the distribution in the (x–z) plane (bottom diagram) shows swirling motion around the necks of the hairpins.
Figure 3: Left: enlargement of the sub-volume indicated by the red box in figure 2, showing arch vortices around a low speed zone; Right: corresponding vector plot in the (x–y) and (x–z) cross-sections.
Low-pass filtered velocity fields are shown in figure 4 and return predominately streamwise and wall-normal vortices, which are visualized by the 2D swirling strengths λci,x and λci,y, respectively. It can be seen that both types of vortices occur adjacent to the low speed zones. Streamwise vortices are typically inclined at 5 degrees with the wall and are about 0.8δ to1.0δ long. Wall-normal vortices often occur in counter rotating pairs on opposite sides of the low speed zones, which is the typical hairpin signature in the (x–z) plane. Streamwise vortices have been frequently observed to terminate in the wall-normal direction, so they may be considered as legs to cane or hairpin structures. Applying the Q-criterion instead of the 2D swirling strength returns the same vortex structures but merged, which makes the interpretation of the results more difficult.
Figure 4: Large-scale vortical structures (magenta) detected by wall-normal swirling motion are revealed after low-pass spatial filtering of the velocity field.
To illustrate how the vortices are organized relative to each other, figure 5 shows a low-speed zone (blue) extending upstream of a single large-scale cane vortex, with only part of the neck (magenta) inside the measurement volume. The low-speed zone extends down to x/δ = 2.6, where u is just above the applied threshold for the blue isosurface and is approaching the local average velocity. Over the low-speed zone several smaller-scale arch and cane shaped vortices (green) are observed. The most downstream vortices (denoted as ‘canes’ in the figure) appear slightly larger and more distorted compared to the upstream arches. This suggests that the smaller scales occur, or are formed, on the low-speed zone associated to the neck and leg of the large-scale cane (or hairpin). The neck and
legs of these large-scale hairpins create long low-speed zones, which then connect to form the very long low-speed zones reported in literature (e.g., Kim & Adrian 1999, Hutchins & Marusic 2007, Ganapathisubramani et al. 2007). Smaller-scale hairpins in turn, are located on top or inside the low-speed zones.
Figure 5: Large- and smaller-scale vortices observed around a short 1.4δ low-speed zone. Blue represents
part of a low speed zone (u < 0.84Ue), green is a Q-isosurface indicating vortical motion in the unfiltered velocity and magenta is an isosurface of the wall-normal swirl in the low-pass filtered velocity, which indicates the neck of a large scale cane.
Results: Incident shock wave/turbulent boundary layer interaction
Figure 6 portrays typical examples of the returned instantaneous flowfield of the boundary layer interacting with an impinging shock wave (Humble et al. 2008). Three values of streamwise velocity isosurface are displayed; high-speed (0.9U∞) in red, intermediate velocity (0.75U∞) in green, and low-speed (0.55U∞) in blue. Figure 6 shows that the previously observed three-dimensional low- and high-speed regions enter the interaction, where a clear deformation of the shock region in response to these large-scale structures may be observed. This is consistent with the work of Ganapathisubramani et al. (2007) in their compression ramp interaction, who observed that the shock-induced separation region conformed to alternating very long regions of low- and high-speed fluid within the incoming boundary layer. This results in a variation in its streamwise location, as well as a spanwise rippling [figure 6(right)], as suggested by Wu & Martin (2008) in their DNS of a compression ramp interaction.
Figure 6: Results of tomographic PIV investigation of a shock wave/turbulent boundary layer interaction. Three values of streamwise velocity isosurface are displayed; hig h-speed (0.9U∞) in red, intermediate
velocity (0.75U∞) in green, and low-speed (0.55U∞) in blue.
Some key phenomenology is highlighted in figure 7 using isosurfaces of vorticity magnitude. The results show an incoming boundary layer populated with numerous regions of concentrated vorticity of various size. They appear in a quasistreamwise alignment, similar to the observations made by Ringuette et al. (2008), who visualized three-dimensional hairpin packets in a supersonic boundary layer using DNS. They again appear associated with the relatively low-speed regions. In contrast, relatively high-speed regions are typically absent of such structures, and exhibit a spanwise sinuous or undulating motion, appearing to meander in-between the surrounding vortical structures. As the interaction region is approached, Q2 (u′ < 0, v′ > 0) events, or bursts, within the reflected shock wave region may be observed. The reflected shock wave region is also the nucleation site for the onset of vorticity across the observed span of the interaction. Moving downstream, the change in vortical structure pattern as a result of the interaction is dramatic, with vortical structures typically losing their identity throughout the interaction.
Figure 7: Overview of interaction phenomenology. Transparent vorticity isosurfaces of ׀ω׀δ/U∞=1 are
shown. Velocity vectors with a convective velocity of 0.8U∞ are shown along with flooded streamwise
velocity contours.
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