time-resolved 3d-ptv analysis of near wall reverse flow...

18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016

Time-Resolved 3D-PTV Analysis of Near Wall Reverse Flow Events in APG

Turbulent Boundary Layers

Matthew Bross1,* and Christian J. Kähler1 1: Institute of Fluid Mechanics and Aerodynamics, Universität der Bundeswehr München, Germany

* Correspondent author: [email protected]

Keywords: Turbulent Boundary Layers, Reverse Flow Events, 3D-PTV

ABSTRACT

In this investigation, local reverse flow features rarely present in the viscous sub-layer of turbulent boundary layers with zero pressure gradients (ZPG) were analyzed in an adverse pressure gradient boundary layer (APG) with the aim to resolve their frequency of occurrence, characteristic size, but also to examine the fundamental causes leading to their appearance. Therefore, particle images in a wall parallel field of view were recorded with two high speed cameras in a stereo configuration and quantitatively evaluated with a time resolved three dimensional particle tracking (TR-3D-PTV) algorithm. From this analysis, the Lagrangian trajectories of tracer particle from two data sets of 55 000 images were adequately resolved in the linear part of the boundary layer down to a wall normal distance of z+ = 1.5. The visualization of specific particle tracks allows for the examination of reverse flow events in the near-wall region with high confidence if a number of important experimental features are taken into account. Similar to the ZPG case it was found that the reverse flow events occur still relatively rarely under the action of the pressure gradient investigated here (only 0.14% for the combined data sets of 110 000 images) but their size can become quite large relative to the observations in boundary layers without pressure gradient. Furthermore, instantaneous measurements of reverse flow events show that these events are associated with the motion of low momentum streaks in the near wall region but moreover, also low momentum turbulent superstructures in the logarithmic region of the turbulent boundary layer flow seem to play a significance role in the generation of reverse flow events. This explains the observation that these reverse flow events appear frequently in groups. Moreover, it was also observed that some of the reverse flow events are associated with streamwise vortices inside low speed streaks. This can be explained by the tilted nature of these vortices with respect to the main flow direction. However, the reverse flow events associated with tilted streamwise vortices inside low speed streaks seem to be smaller in size than the aforementioned reverse flow events. The results and discussion will serve to better understand the interaction of coherent flow structures leading to reverse flow events.

1. Introduction Turbulent boundary layers are critical for the aerodynamic performance of many technical

components and the physical understanding for these types of flows is of great scientific and technological interest and importance. While the turbulent flows along a flat plate with zero pressure gradients were investigated in great detail in the last decades, the effect of a pressure gradient is by far less understood. Also the transition from the fully attached to the partly and


fully separated flow state is widely unknown in all its details. In this work we will focus our attention towards the very near wall region as flow separation always begins at the wall. Of particular interest for the present investigation are the relatively rare instances of very small localized reverse flow events. They might be the nucleus for the generation of macroscopic flow separation in adverse pressure gradient boundary layers, and their connection with large scale turbulent flow structures such as near wall low speed streaks and large scale turbulent superstructures in the logarithmic region of the flow might help to better understand the complexity of near wall flow phenomena. In recent years, the numerical prediction of reverse flow events in channel (Leaners et al. (2012)) and turbulent boundary layer flows (Stalwart & Coleman (1997)) has achieved strong attention (Cardea et al. (2014)). As the spatial extent of these events is very small according to (Cardea et al. (2014)), and their occurrence extremely seldom (Schlitter & Arul (2010)), their detection in experiments was quite challenging. However, in recent publications by Bruckner (2015) and Willet (2015) their existence could be confirmed experimentally by using micro pillars (Große & Schroder (2007)) and long-range micro PIV techniques (Kähler et al. (2006)).

The aforementioned numerical and experimental studies were performed at relatively low Reynolds numbers (Reτ <2000) and zero pressure gradients. The probability of such events occurring was measured to be around 0.01% (Willert (2015)), which makes further statistical analysis of reverse flow events difficult due to the low number of samples. Furthermore, the experimental investigations yield only information about the footprint of the reverse flow events onto the wall shear stress Brücker (2015) and the characteristics of the structures in an arbitrary slice selected by the light-sheet used for the planar PIV investigation by Willert (2015). A more detailed analysis requires 3D velocity measurement techniques to fully resolve the events in space and to avoid bias errors PTV algorithms are better suited than PIV evaluation techniques according to Kähler (2012 a,b). However, this is not a simple task because of optical access, the high recording frequency needed, wall reflections and seeding requirements for instance Schröder et al. (2015)

The relationship between the rare near-wall flow effects with coherent large scale motion in the near wall and logarithmic region of the turbulent boundary layer is also of strong interest as a connection would allow for the manipulation of these reverse flow events by means of macroscopic flow control methods. This may be beneficial to delaying flow separation (by reducing the number of reverse flow events) or by decreasing the viscous drag of fully attached flows (by increasing the appearance of reverse flow events). It is possible that the reverse flow events are associated with the motion of near wall low speed streaks (Kline et al. (1967) and


Smith & Metzler (1983)) or even low momentum superstructures (Buchmann et al. (2016)) but, this has not been demonstrated experimentally or numerically so far. However, as the low speed streaks appear at any near wall location very frequently in time, in contrast to reverse flow events, we assume that near wall low speed streaks are just a necessary condition for the appearance of near wall flow events. Something else is necessary and we have hypothesised that a specific interaction between near wall low speed streaks and large scale low momentum superstructures (Buchmann et al. 2016) is necessary to generate the rare reverse near wall flow events. Large scale meandering streamwise oriented structures with alternating high and low speed streaks, referred to as superstructures, are described in Adrian et al. (2000) and Tomkins & Adrian (2003). Further evidence of these large scale structures provided by PIV, is discussed in Ganapathisubramani et al. (2003) and Hambleton et al. (2006). The highly resolved LES simulations by Schlatter et al. (2010) and the hot-wire measurements performed by Hutchins & Marusic (2007 a,b) showed that these superstructures have a span-wise average periodicity of 1δ and they can be up to 15δ ‒ 20δ length in the streamwise direction. Additional analysis by Hutchins & Marusic (2007b) and Mathias et al. (2009) showed that low frequency meandering superstructures appear to modulate near wall turbulence production cycle. This was confirmed by Buchmann et al. (2016), for measurements at large Reynolds numbers (Reτ = 5000−9500), where the superstructures were resolved using PIV while simultaneously recording the foot print of the structures on the wall by time resolved pressure probes. Although pointwise measurements provide velocity measurements with low uncertainties, full field measurements via quantitative optical techniques (Kähler et al. (2006), Kähler et al. (2012), Cierpka et al. (2013b), Reuther et al. (2015), Willert (2015), Knopp et al. (2015), Schröder et al. (2015)) provide more information about the characteristics of the near wall flow structures and their interaction with the outer part of the turbulent boundary layer flow. In the investigation presented herein, the topology and statistics of near wall reverse events will be discussed and their connection with the aforementioned large scale coherent structures is outlined. As these reverse flow events appear very seldom in low Reynolds number turbulent boundary layers along flat plates with zero pressure gradient we examine these structures at larger Reynolds numbers and under the effect of an adverse pressure gradient to make a statistical analysis of the rare reverse flow events possible. This also allows us to examine if the rare reverse flow events are universal or if multiple events exist with different topology. Furthermore, we will be able to examine their scale and dynamics and if the events appear randomly in space and time or in packets with a characteristic frequency. To resolve the details of


the near wall flow a novel three-dimensional tracking technique is used to record time resolve the flow in the viscous sub layer The working principle of the technique and specific technical considerations to make this type of near wall experiment possible are discussed and the process of resolving the mean flow field is provided. In particular, flow information in the spanwise direction is available, which is absent from previous two-dimensional PIV studies. 2. Experimental Systems

Turbulent boundary layer experiments were performed at the Universität der Bundeswehr Munich in the Atmospheric Windtunnel Munich (AWM). The Eiffel type wind tunnel has a 22 m long test section with a cross section of 2 × 1.8 m2. A 7 m long polished aluminum boundary layer model consisting of two S-shaped deflections on either end of a 4 m flat plate zero pressure gradient (ZPG) section, was installed along the side wall of the wind tunnel. The adverse pressure gradient (APG) region (downstream of the ZPG part) was fitted with a glass viewing window of size 0.26 × 0.59 m2, see Figure 1 View A. The coordinate system (x,y,z) defined in View A corresponds to the wall parallel direction in the APG, spanwise direction, and wall normal direction respectively. The X-direction indicates the streamwise distance along the windtunnel, starting at the beginning of the model. The pressure coefficient and gradient along the model at this Reynolds number is shown in Figure 2. These qualification measurements gathered data at pressure taps along the model are supplemented with numerical data in the adverse pressure gradient region because the uncertainty of the experimental pressure measurement increased with decreasing flow velocity in that region (Reuther (2015)).

In order to perform quantitative flow visualization, a local seeding system was installed upstream of the boundary layer wall, providing uniform seeding throughout the boundary layer. A local seeding system flush mounted in the side wall of the wind tunnel ~2 m before the aluminum model was implemented to avoid a contamination of the wind tunnel with the large amount of seeding produced by a global seeder which may lead to unwanted disturbances of the flow (Bradshaw (1964) & Bradshaw (1965)). The local seeding system was constructed by covering a 50 × 1000 mm2 slit in the wind tunnel wall with a large wooden box. On the inside of the tunnel the slit was covered with an aluminum plate having 2 mm holes in a regular arrangement that was made flush to the wall. The wooden box connected at the outside wall of the windtunnel was then attached to conventional impactor seeding generator creating DEHS particles with an approximately 1μm mean diameter, Kähler et al. (2002). The box is filled with tracer particles which are sucked through the aluminum grid into the boundary layer due to the pressure difference in the box and inside the tunnel. This system is ideal for boundary layer


experiments, as the seeding is fed directly into the boundary layer. Furthermore, the location and concentration of the tracer particles can be easily varied by adjusting the position and number of openings in the aluminum plate and the settings of the seeding generator. Finally, the disturbance of the flow is minimal as the particles are sucked out of the reservoir by means of the slightly lower pressure in the wind tunnel test section and a homogeneous concentration of particles could be reached at the measurement location because of the natural turbulent mixing of the particles inside the boundary layer along the model. For the measurements present herein, the average seeding concentration in the flow volume was Npp = 0.001.

The tracer particles in the APG region were illuminated in a wall parallel plane by a continuous wave laser (Kvant Laser) with maximum output power of 8 W and 532 μm wavelength. The laser beam was formed into a uniform sheet of 40 mm width and thickness of 1 mm and aligned directly adjacent to the wall. This beam profile was determined by using DataRay Inc. WinCamD-LCM1C beam profiling camera. Due to the quality of the glass, the cleaning procedure before the experiments, and the wall parallel orientation of the light sheet, surface reflections did not appear. High speed particle image sequences were captured by two a high-speed CMOS camera with 36GB of RAM (Dimax-S4, PCO GmbH) mounted in a 30 degree (with respect to wall normal) stereo configuration behind the glass viewing window in the APG (Fig.1). Using a 50 mm/f2.8 Zeiss objectives and Scheimpflug mounts, the resulting pixel size in the center of the FOV was ~25 µm/pix. By dividing the pixel pitch of the HS camera (11 µm/pix) the resulting magnification in the center of the FOV was M = 0.44. The camera field of view (FOV) was cropped to a 576 px by 800 px window so that long time sequences could be recorded and stay within the RAM limitation of the camera. Two time resolved sequences of 55 000 images were captured at 8.2 kHz recording frequency. The exposure time for the CCD array was set to 24 μs, in order to avoid particle image streaks.

Due to upper limitation of the optical set up, experiments were only performed at a freestream velocity of 9.5 m/s (approximately 12 m/s over the model) corresponding to a Reτ = 5000. The boundary layer thickness of δ = 300 mm at the measurement location, was determined from large field qualification experiments performed on this model. At larger Reynolds numbers, the particle displacement between frames became too large to accurately track them. Also, as the recording frequency increases, the light energy density per frame will decrease, and hence lower the signal to noise ratio for the particle image. The methods for reconstructing the flow volume and the time resolved particle tracking is discussed in the next section.


Figure 1: Plan view of boundary layer model in AMW. High Speed Stereo measurements were performed in adverse

pressure gradient (APG) section, see View A. The Field of View (FOV) volume (indicated by red rectangle) is 8 × 20

× 1 mm3. The coordinates (x,y,z) correspond to the wall parallel direction in the APG, spanwise direction, and wall

normal direction respectively.

Figure 2: Pressure coefficient and gradient values from experimental and numerical results across the boundary

layer model (X-direction, see Fig 1.) for 10 m/s freestream velocity.

3. Volume Reconstruction and Particle Tracking

Determining the spatial particle locations was performed using a particle matching and triangulation algorithm developed by Fuchs et al. (2016). An overview of the steps involved is as follows. Firstly, the particle images in each image must be detected by subtracting out the average background intensity and subtracting the sliding minimum intensity filter so that only locally bright pixels remain. The detected particle images are then fitted with 2D Gaussian


profile to determine sub-pixel center location. After the particle locations are determined for each camera, matching particle images are identified based on epipolar geometry, i.e. possible particle images matches are searched in a defined area in the proximity of the epipolar line on the second sensor for each particle image on the first sensor. The uniquely matching particle images are then triangulated to get the spatial particle location (x,y,z) by means of the optimal triangulation method, Hartley & Sturm (1997).

The trajectories are determined using a three dimensional time resolved particle tracking algorithm (3D-TR-PTV). The core working principle of this tracking code is based on a nearest neighbor approach where particle images are assigned to a specific track based on global displacement bounds, locally taking into account local acceleration limits, and measurement uncertainties in all three spatial directions, Cierpka et al. (2013a). If a particle is recorded over a sequence of images, and the position of each particle image adheres to global and local tracking parameters, all of the particle images in that trajectory are assigned a single integer identification number. In other words, each identified trajectory, consisting of several particle images, is assigned a unique track number (track ID) Furthermore, the data presented herein is time resolved, and therefore algorithm also checks the validity of track IDs by comparing particle images at time t with t − 1 and t + 1.

After the track IDs assigned, the displacements between particle images along these tracks are computed. First a polynomial is fitted to the points in each track and a displacement vector is calculated by interpolating the positions to that curve. This interpolation to a polynomial curve also acts as a low pass filter, filtering out small particle image positions errors. For shorter tracks, consisting of 1 or 2 displacements, a linear interpolation is used. More in depth details about this type of tracking and interpolation are outlined in Cierpka et al. (2013a). With this technique many of the particle images from the original volume are assigned track IDs. In the data presented herein 88% (~4.5 × 107 out of ~5.1 × 107 particle images) of the particle images in the reconstructed volume were assigned trajectory of minimum length 1, i.e. track length = 1 means that two successive particle images of the same particle are connected and the displacement between these particle images is calculated. Moreover, the distribution of track length for both data sets as percentage of total number of vectors is shown in Figure 3.

Figure 3 shows that about 14% of the trajectories are only length 1 or 2 which consist of 2 or 3 particle images respectively. It must be noted that track lengths greater than 30 are present, up to a maximum value of 110, but the probability of such a track occurring is very small when considering the entire data set and therefore was not plotted in Figure 3.


In order to understand the distribution of trajectory lengths an ideal rectangular measurement volume with a uniform light intensity distribution can be considered, according to Figure 4. It can be expected that the longest possible continuous tracks of length d, like Track A, appear if a particle enters the volume at the beginning of the image sequence and disappears at the end during the image sequence. If the measurement time is sufficiently long, then the longest tracks are associated with particles that move close to the wall with a low velocity. Therefore, it follows that the faster the particle’s motion, the shorter the track length will be. Trajectories consisting of only a few particle images can occur when a particle enters the measurement domain at the end of the recording sequence or if a particle is inside the measurement domain at the beginning of the image acquisition, see trajectories labeled B in Figure 4. However, when considering the length of the recorded image sequences of the present data sets, these types of trajectories should be considered negligible and therefore not responsible for the large peaks in Figure 3.

Figure 3: Probability density distribution of trajectory length for all vectors from both data sets.

More likely are trajectories of small length at the boundaries of the measurement volume

when particles associated with a longer trajectory slightly enter the light sheet and are detected, see particles labeled C. In the present case, the probability of detecting short particle paths at the boundaries will increase because of the thin extent of the volume in wall normal direction and the turbulent nature of the flow under investigation. Furthermore, the measurement volume created by the laser was not exactly rectangular, rather more elliptical, which will also contribute to the detection of short particle paths near the boundaries.


Moreover, another cause of short particle path occurs when two particles overlap in the measurement volume. This will cause a matching disparity during the volume reconstruction which will break longer tracks into separate tracks of smaller length, as shown by track D. This effect can occur quite often because of the relatively dense seeding concentration inside the measurement volume. Considering the previous discussion, it is reasonable to use the track length as detection criteria to remove valid but short particle tracks from the flow analysis.

Figure 4: Idealized measurement volume and particle trajectory types. Hollow circles indicate particles that are

outside the volume or undetected and filled circles represent detected particles.

4. Mean Flow Field

Before starting the flow analysis of the mean field, it is important to first look at the particle image distribution and displacements in the wall normal or z-direction as displayed in Figure 5. The top figure shows all trajectories of any length, which accounts for ~22 million vectors. In the bottom figure, trajectories with length of two or shorter are removed (~4 million points deleted). It can be seen that the characteristics of the distribution is not changed by the short tracks as expected from the analysis above. Furthermore, it is visible that the wall position during calibration (while the wind tunnel is not operating) is located at z = 0 mm while during the experiment the boundary layer model translates about 0.1 mm in positive z-direction, as expected from the negative pressure difference. Therefore, all points (particle images) below a straight line at z = 0.1 mm are outliers and are disregarded (~5000 points) for the flow analysis.

Points can then be collected into in bins spaced in the z-direction and extending over xy-planes. For the mean flow results, bins of z-direction spacing 12.5 µm were created. The discreet and continuous distribution of stream wise displacements tracks in each bin is displayed in Figure 6. In the near wall region it appears that there is a sharp decrease in points. This is due to the lack of sufficient seeding concentration in the very near wall region. The low seeding concentration may have a strong effect on the statistical quantities because outliers in this region, with large displacement values significantly alter the mean value in these bins. To account for this, a continuous distribution of each bin was fit to the points with by means of a Gauss


function, see red curve in in the lower image of Figure 6. With this fit applied, the mean field in each bin can be calculated by either taking the peak of the Gauss curve or only considering values within 2σ. The mean field from averaging the discreet points and using the continuous representation is compared in Figure 7 to highlight the significance of this effect.

Figure 5: Wall normal (z-direction) distribution of streamwise displacement (∆x). Top figure displays all vector

lengths which is approximately 22 million points (particle images). In the bottom figure trajectories with length

greater than two are removed (~4 million points) and all outliers below the wall location are also removed.

Clearly visible is the strong deviation of the data points from law of the wall at z+ < 2

(green dots) where the particle seeding is lacking, (see Figures 5, 6, and 8). If the continuous representation (orange and purple) is used to estimate the mean velocity with the peak of the fit


or only considering values within 2σ, a much better agreement with the universal law can be achieved for z+ < 2. By using the local mean value estimated from the continuous representation of the data also the velocity fluctuations will be correctly determined while in case of using the unfiltered data, the fluctuations would be largely biased because of the wrongly estimated mean velocity values.

Figure 6: Streamwise displacement (∆x) distribution in wall normal (z-direction) bins of 12.5 µm spacing. Top figure

represents the discrete distribution and bottom figure displays the overlay (red line) of a continuous distribution

based on a Gauss function fit.


Due to having reliable data points in the linear region (z+ = u+) of the turbulent boundary

layer flow, calculating the viscous scaling is straight forward. A linear fit of 𝑢 vs.𝑧, where 𝑢 =𝑢 + 𝑢& and 𝑧 is the average bin position in the z-direction, allows for the calculation of 𝑢' =

𝜈 𝑑𝑢𝑑𝑧 *+,

and the z-intercept indicates the wall location. Therefore, u+ = 𝑢/𝑢' and z+ = 𝑧𝑢'/𝜈

can directly be calculated. With this experiment we were able to achieve relatively good mean values at approximately 1.5z+. Our results show that 𝑢' = 0.24 and the wall location z0 = 0.12 mm. Therefore, the viscous unit 𝜈/𝑢' = 65 µm.

Figure 7: Mean flow in viscous units for averages of discrete data and continuous fits.


Figure 8: Effective seeding density in wall normal bins for combined data sets.

5. Reverse Event Detection and Characterization

It is clear that the extension of the near wall flow events in wall normal direction is quite small and due the statistical variations of the events in size, their extent in wall normal direction will vary as well between different events. This means that the probability of detecting these events will decrease with increasing wall distance until no events will be observable anymore. Consequently, the probability in finding these events is the largest at very small wall distances. However, due to the drop of the seeding concentration towards the wall, as indicated in Figure 8, the likelihood in detecting these events in real measurements also decreases towards the wall and a maximum must exist at a certain wall distance were the detectability becomes largest. For a statistical analysis of these events it is important to know this maximum, in order to minimize bias effects in detecting the number of events.

The first step for identifying reverse events (flow in the negative streamwise direction) involves filtering out vectors that are less likely to be associated with reverse events and the second step is to determine the location in the wall normal direction where they occur. The probability density distribution of track lengths for reverse events in Figure 10, shows that almost half of negative streamwise displacements detected only have a length of one. Some of these one point trajectories may be valid, i.e. particle images located at the edges of the event, but since it is expected that reverse events occur close to the wall and at slow velocities, it is expected that only the longer trajectories yield relevant physical information about the events. Therefore, for further analysis only negative streamwise vectors in trajectories of length>1 are considered to be physically significant.


Figure 10: Trajectory length of vectors with negative streamwise displacements.

The distribution of these negative streamwise displacement vectors in z+ direction is

shown in Figure 11. The PDF of reverse event vectors indicates that more than 85% of these events occur less than z+ = 6. In other words, the drop in probability in the very near wall region shown for the result presented herein, is directly associated with the lack of seeding in that region as pointed out before. However, the distribution shows nicely that the maximum number of events can be detected around z+ ≈3 according to Figure 11.

Figure 11: Negative streamwise trajectories, with length longer than one, location with respect to the wall.

Now that the statistically important reverse events have been identified and the location

in the wall normal direction has been identified, the probability of these events appearing with respect to all displacements for 1 < z+ < 6 (2σ distance from distribution in Figure 11) can be ascertained from Figure 12. Even for this range of z+, the probability of a negative streamwise displacement occurring is relatively low, 0.0014 or 0.14%. This value of course would presumable increase slightly if the seeding concentration was consistent in the very near wall region (z+<2) as discussed above. However, the low values indicates that the pressure gradient under investigation has only a minor effect on the number of reverse flow events compared to the ZPG boundary layer flow.


Figure 12: Probability density function for streamwise displacements at wall locations 1 < z+ < 6. Negative values

represent a probability of 0.0014.

6. Reverse Even Flow Visualization In the preceding sections, efforts to qualify the experimental data and assess statistical

properties have been made. Keeping that analysis in mind, it is important to now characterize the flow structure during these reverse events. The first step involves determining the temporal location in the data set where reverse event trajectories appear. Figure 13 provides a map that identifies the image ranges where reverse events occur. Negative displacement vectors are grouped into bins of 50 images for one data set of 55 000 images. Bins are filtered by removing bins that only have one unique trajectory inside and if that trajectory consists of less than three points. This means that reverse flow events which are only sampled by one single particle image or only at the outer edge of the events are not considered for the analysis as both cases yield very little information about the topology and dynamics of the events. First it should be noted that many intervals exist were no reverse flow event exist and the length of the intervals can be quite large, as expected from previous investigations. Second, it appears that reverse flow events appear in groups. This does not necessarily mean that they interact in these groups, but once a reverse flow event appears it is likely to see more events within a short time frame. Third, from the amplitude and distribution of the signal in this plot it is evident that there are several


different classes or types of reverse events in terms of time duration and number of vectors. Therefore two large, one medium, and one small peak, labeled L1, L2, M, and S accordingly, were chosen to plot the particle trajectories for comparison. These events are classified broadly, meaning that size of an event is designated based on the number of unique negative trajectories and vectors, which would only be fully correct for a homogeneous seeding concentration.

Figure 13: Number of negative displacement vectors in 50 image bins for data set of 55 000 images. Bins are filtered

by removing bins with only one unique trajectory and if that trajectory has less than points for that range of 50

images. Fifty images span a time of approximately 0.006 s.

In Figure 14, two of the larger peaks (L1 and L2, Figure 13) are chosen to visualize the

particle trajectories. Particle trajectories for image ranges between 4500−4600 and 42880−42980 are plotted with blue coloring representing negative streamwise velocity components and red coloring for positive streamwise velocities. Also displayed is the number of unique trajectories and the total number of negative velocities vectors in the plotted image range. For top left image the reverse event (L1, see Figure 13) clearly appears to be a collection of several trajectories with a streamwise (x) and spanwise (y) scale of approximately 4 and 6 mm in the x and y directions respectively. It should be noted that the size of the event is much larger than reported in the literature (Cardesa et al. (2014)). However, there are individual trajectories outside this region which may be parts of smaller reverse events. Looking at the flow field surrounding reverse event (top right image), the near wall low and high speed streaks are clearly visible. In this particular measurement there are three low momentum streaks (indicated by the relatively small


distance between particle positions) spaced in between fast moving streaks (more straight particle trajectories). The distance between the fast moving streaks is around 75 y+. It is obvious that the large reverse flow event is associated with a low speed streak but also the small reverse flow events are at locations were low speed streak are present. Thus we conclude that low speed streaks are a necessary condition for the existence of reverse flow events.

For comparison another large reverse event (L2, see Figure 13) is displayed in the bottom two images of Figure 14. Again, the reverse event appears to be a collection of several trajectories with a streamwise (x) and spanwise (y) scale of approximately 8 mm and 4 mm respectively. However the full flow field (bottom right) image appears remarkably different than the L1 event. In the region in close proximity to the reverse event, a distinct band of low momentum fluid appears. However, above this region y > 0 mm, the fluid is moving relatively fast and appears unidirectional form in a streamwise orientation. In contrast to the top images, a pattern of spanwise oriented momentum streaks is not clearly visible because of the larger convection velocity, but a closer look indicates that the streaky nature of the flow still exists. The larger convection velocity might be associated with a large scale superstructure moving with a velocity faster than the mean velocity (Buchmann et al. (2016)). Due to the raise in convection velocity by high momentum superstructures it can be assumed that reverse flow events are suppressed. This shows that the superstructures in the logarithmic part of the boundary layer can have a significant effect on the near wall flow structures.

In Figure 15, a medium reverse event (M, Figure 13) is selected for visualization. This medium event comprises of 15 −16 unique trajectories with around 80 vectors distributed throughout the unique trajectories. In this case, trajectories appear grouped in a defined spatial location and extend over and area of 4 mm by 4 mm in the streamwise and spanwise directions. Looking at the rest of the flow field, the region affected by the reverse event is quite large again. In this case, a distribution of fast moving streaks is visible with spacing around 150 y+. Remarkable is the significant spanwise motion of this event which was not observed in the other figures. It seems clear that the large spanwise motion must be associated with small longitudinal vortices. If the axis of a streamwise vortex is slightly tilted with respect to the mean flow direction, these longitudinal vortices can generate reverse flow events provided the vortex travels with a sufficiently low convection velocity, which is possible when the vortex is imbedded inside a low speed streak.


Figure 14: Two examples of larger reverse events for image ranges 42890−42980 and 4500−4600 (L1 and L2, Figure

13). Left images only display vectors with negative (blue) streamwise components and right images display all other

vectors (red). Freestream direction is from left to right.

Figure 15: One example of a medium reverse event for image ranges 1513-1613 (M, Fig. 13). Left images only display

vectors with negative (blue) streamwise components and right images display all other vectors (red). Freestream

direction is from left to right.


Figure 16: One example of a smaller reverse event for image ranges 29589-29689 (S, Fig. 13). Left images only

display vectors with negative (blue) streamwise components and right images display all other vectors (red).

Freestream direction is from left to right.

Finally, an example of a smaller event, (S, see Figure 13), is provided in Figure 16. This smaller event consists of only ten trajectories and 38 vectors, which is much smaller than the large and medium examples shown in Figures 14 and 15. For this range of images a grouping of reverse flow trajectories appear between y = −5 to −3 mm and x = 0 to 5 mm. These events correspond again with a larger low momentum region in the full flow field shown in the right image. Again, in the full field low and high momentum streaks in the spanwise distribution are visible. 7. Conclusions

The work presented herein, investigated the rare reverse flow events in an adverse pressure gradient turbulent boundary layer flow at Reτ = 5000 by using a novel time resolved 3D-PTV technique. The results show that these events appear mostly in the wall region below 0< z+

<6. Furthermore, the probability of a reverse flow vector occurring in the region below z+ = 6 was found to be around 0.14% which indicates that there is only a small increase in number of reverse events compared to the zero pressure boundary layer cases reported in the literature. It must be stated however, that in the very near wall region (z+ < 2) the statistics are influenced by the lack on seeding concentration in that region. Therefore, the probability of a reverse event occurring at the pressure gradient considered here will likely increase if in the very near wall region if the seeding concentration is sufficient.

The physical characteristics of reverse events were discovered by observing trajectory plots at several representative image ranges. From these images it was demonstrated that there exist several different forms of these events in terms of the total number of adjacent trajectories and spatial extent. It was shown that for the larger events with several closely grouped trajectories, the spatial extent in both spanwise and streamwise directions was on the millimeter scale which is larger than the dimensions given in the literature.

In all cases of reverse flow events displayed, an extended region of low momentum fluid was observed around the reverse events which was associated with the well know near wall low speed streaks. Therefore, it can be concluded that low speed streaks are a necessary condition for the appearance of reverse flow events. But the low detectability of the reverse flow events indicates that another phenomenon must take place simultaneously to generate the conditions


which may lead to these rare events. The results indicate that a low momentum superstructure superimposed on the low speed streak, which has a sufficiently low momentum, creates the ideal condition for the generation of reverse events. On the other hand, when high momentum superstructures are superimposed on the near wall low speed streaks the convection velocity increases and reverse flow events are suppressed. Due to the length of the high momentum superstructures it is evident that long intervals exist where no reverse flow events can be observed. However, when a superstructure with sufficiently low momentum is present at the measurement location, groups of reverse flow events have been observed frequently.

In addition, some reverse flow events were associated with a strong spanwise velocity component. This was caused by small longitudinally oriented vortices in the near-wall flow. However, the regions of strong spanwise flow velocity are again correlated with elongated regions of low momentum fluid which indicates that the longitudinal vortices resided within the near wall low speed streaks. Therefore, reverse flow events can occur as well when the axis of the streamwise vortices is slightly tilted with respect to the mean flow direction, generating flow in both the spanwise and upstream directions. However, this only creates a reverse flow event if the convection velocity of the streamwise vortex is sufficiently low. Therefore, these events could be only observed when the longitudinal vortex was embedded in a near wall low speed streak and travels with the low velocity of the streak.

The results clearly show that reverse flow events are not universal and it could be shown that their generation requires a direct interaction of near wall low speed streaks and large scale turbulent superstructures of sufficiently low momentum. However, because the velocity deficit required by superimposing both low momentum structures is quite large, the total number of events will be low as observed herein. However, whenever the specific conditions are reached, multiple reverse flow events can be generated one after another. This explains why these events appear on different time scales. References

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time-resolved 3d-ptv analysis of near wall reverse flow...

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