tomographic piv and planar time-resolved piv measurements...

16th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 09-12 July, 2012

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Tomographic PIV and Planar Time-resolved PIV Measurements in a Turbulent

Slot Jet

Artur V. Bilsky1,2, Vladimir A. Lozhkin1, Dmitry M. Markovich1,2*, Maxim V. Shestakov1,2, Mikhail P. Tokarev1,2

1: Institute of Thermophysics, Siberian Branch of RAS, 1 Lavrentyev Avenue, Novosibirsk, 630090, Russia

2: Department of Physics, Novosibirsk State University, 2 Pirogova Str., Novosibirsk, 630090, Russia * correspondent author: [email protected]

Abstract The structure of a quasi-two-dimensional turbulent jet in a narrow channel was investigated experimentally in this work. Study of spatio-temporal flow structure was produced by the Time-resolved PIV technique. The 3D flow structure in the near field of the jet was studied by Tomographic PIV. Secondary flows in the bounded jet were obtained by Tomographic PIV for the first time.

1. Introduction Jet flows are one of the most common forms of fluid dynamics in technological and natural systems. Recently, researchers are paying particular attention to micro and mini jets in a confined space. This is due to general trends in the development of small-scale technical systems. The jet in a narrow or slot channel has a number of features that significantly distinguish it from free jets and flows in channels. The presence of the bounding surfaces leads to different characteristic scales: small-scale three-dimensional flow with a maximum scale of the order of a channel depth and quasi-two-dimensional large-scale flow with the characteristic scales greater than the channel depth (Bilsky et al. 2007). The features of such flows allow investigating the properties of quasi-two-dimensional turbulence and the mechanisms of interaction between large-scale two-dimensional structures and small-scale three-dimensional turbulence in a laboratory. Heskestad (1965) showed that the jets in confined channels cannot be described by two-dimensional flow equations. Secondary flows are formed near the bounding planes inside a jet shear layer which lead to a significant three-dimensional flow. Features of the bounded two-dimensional jets have been studied in Foss and Jones (1968). The authors showed that the flat bounded jet is not a superposition of two flows: a boundary layer and a two-dimensional jet. Based on measured velocity distributions in a cross section, the authors proposed a physical model of secondary flows. Later, in the paper Holdeman and Foss (1975) the authors confirmed this effect by the results of hot-wire measurements and direct vorticity strength measurements by a small mechanical turbine. The model assumed that the secondary flows arise from the curvature of the vortex tube, which is formed on an edge of a nozzle. The vortex tube is similar to that formed at the end of the free rectangular jets, but the presence of bounding surfaces leads to the generation of longitudinal vorticity due to bending of the vortex tube near the bounding surfaces. The reorientation of the vortex tube is directly related to its curvature, arising due to the presence of slip at the wall and the velocity gradient near the wall. The authors showed that the secondary flows are completely determined by the longitudinal vorticity. A model based on the curvature of the vortex tube, also confirmed by other authors on the study of three-dimensional wall jet. However, Owczarek and Rockwell (1972) suggest another mechanism of secondary flows in a slot jet. Their model is based on the fact that the sources of secondary flows in the jet flow are rising out of the corners of a rectangular nozzle. The mechanism of secondary flows in rectangular channels, and in semi-infinite angles is well studied and confirmed in many experimental works.


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Discovered and described secondary flows significantly affect the mixing processes and the involvement of fluid in a bounded jet. It is the secondary flows are responsible for three-dimensional effects in a jet (Gordeyev and Thomas, 2000), which lead to a significant mixing across the channel. Thus, the modeling of the bounded jets within two-dimensional approach does not allow describing all features of a flow. With the development of contactless optical techniques for flow field diagnostics many researchers have once again expressed an interest in bounded jets (Dracos et al. 1992; Nakoryakov et al. 1998). In Dracos et al. (1992) the effect of the channel height on the structure of the flow was investigated by laser-Doppler velocity. The Reynolds number in the experiments, calculated from the width of the nozzle was 10 000, the ratio of the width of the nozzle d to the depth of the channel h varied from 1:2 to 1:36. According to the measurements of velocity profiles and velocity fluctuations, the authors identify the three characteristic regions: near, middle and a far field in a slot jet flow. Here the authors adhere to the model proposed in Holdeman and Foss (1975), and point to the fact that the secondary flows strongly depend on the shape and parameters of the nozzle and begin in the near field of the jet. These secondary flows have a significant effect on the mean field, where the flow is strongly three-dimensional. In the far field the secondary flows are destroyed. Feature of the far-field is the development of jet instability and the presence of large-scale quasi-coherent structures, which alternate by pairs in a vortex street. The type of the far-field spectrum is the same as for two-dimensional turbulence. In Nakoryakov et al. (1998) the turbulent jet in a Hele-Shaw cell was studied. The difference between this work and the papers mentioned above was the small depth of the channel h, equal to 0.68 mm and 2 mm for a sufficiently large width of the nozzle d, equal to 6 mm and 20 mm, respectively. The authors of this study also point to the three-dimensional phenomenon, but qualitative and quantitative data are not present. By analyzing these works, it can be concluded that data obtained with local methods do not give a complete picture of the flow and may not contain information on the three-dimensional structures. In this paper two measurement techniques were used for investigation of the turbulent slot jet: a planar Time-resolved PIV and a low repetition Tomographic PIV. There are several recent papers describing Tomo-PIV measurements in transitional and turbulent circular and chevron jets (Violato and Scarano, 2011; Khashehchi et al. 2010), turbulent boundary layer (Schröder et al. 2008; Atkinson et al., 2011). The aim of this work is to combine benefits of time-resolved planar and volumetric measurements to analyze complex behavior and a structure of a turbulent jet in bounded geometry. Another objective is to provide quantitative comparison between capabilities of these two measurement techniques for investigation of the specified object. 2. Experimental setup The picture of the experimental setup is shown in Figure 1. The experimental setup is a closed hydrodynamic contour, including a tank, a pump, a flow meter, and a test section. A working section was a narrow channel formed by two transparent plates made of organic glass (with the size of 307x270 mm and thickness of 40 mm), located at a distance h = 4 mm from each other. The nozzle was formed by two flat inserts, which have Witoszynski profile; the nozzle width was equal to d = 10 mm, and the length of the nozzle straight region was 20 mm. Polyamide particle tracers with an average diameter of dp = 20 um were suspended in distilled water. 3. Planar PIV measurements Time-resolved PIV measurements were performed in a single measurement area with the size of 6.5d×17.5d and at three different sections through the channel depth: z = 0, z = 0.25h and z = 0.4h (z = 0 corresponds to a central plane) normal to the slot. The thickness of the laser sheet in the


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measurement area was in the range from 0.3 to 0.5 mm. The thickness was close to a depth of an interrogation box for Tomo-PIV correlation step. A single exposure mode for Re = 10 000 with a maximal frame rate 1.2 kHz, dt = 0.85 ms and a double exposure mode for Re = 20 000 at 625 Hz, dt = 0.45 ms were utilized during the experiment. The Reynolds number was constructed by 2h and the mean flow rate velocity U0: Re = U02h/ν. A high-speed Pegasus PIV Nd: YLF double-cavity laser (2x10 mJ at 2x1,200 Hz) and a high-speed PCO 1200hs CMOS camera are used to obtain instantaneous velocity fields (see Figure 1, a). The image size was equal to 501×1280 px. An iterative correlation multigrid algorithm with continuous shifting of interrogation areas was applied to obtain 3 000 velocity fields for each flow regime. The final size of the interrogation windows is 32×32 px located with 75% overlapping ratio within a grid of 59×157 measurement points. This corresponds to the spatial resolution 4.15×4.38×0.5 mm per one velocity vector. 4. Tomographic PIV measurements Tomo-PIV measurements were carried out in three successive overlapping volumes with the size 4d×3.4d×0.43d (see Figure 1, b). The data were acquired for two Reynolds numbers: Re = {10 000, 20 000}. A number of measurement volume snapshots for each regime which further were used to calculate statistical characteristics of the flow were equal to 500. The “POLIS” measurement system was used, consisting of a double pulsed Nd: YAG laser (50 mJ per 10 ns pulse), four CCD cameras (1360×1024 px, 12 bit) and a synchronizing device. “ActualFlow” software was used to manage the hardware and process the acquired data. The width of the laser beam was 5 mm, so the whole flow area was illuminated. Nikon lenses with the 50 mm focal length were used. The 50×50 mm plain calibration target with reference circles on the Cartesian grid with the 2 mm step between circles was used. A precise traverse system was used to shift cameras relative to the fixed calibration template inside the slot for volumetric calibration.

(a) (b)

Figure 1. The scheme of the experimental setup for planar Time-resolved PIV (a) and Tomo-PIV (b) measurements in a turbulent slot jet, d = 10 mm, h = 4 mm. As for data processing, before the reconstruction step registered projections were preprocessed by subtracting the statistical intensity minimum calculated separately for each view. A reconstructed


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3D object was discretized into 1024×896×128 voxels with the 8 bits quantization level. After lossless LZW compression a pair of 3D objects had a volume size near to 40 Mb. The physical size of a voxel was approximately equal to 0.04 mm3. Volume particle concentration was close to 8.5 part/mm3. Image density at this concentration upon registered projections was 0.045 ppp, which corresponds to source density Ns=0.22 with particle image diameter dp=2.5 px. For tomographic intensity reconstruction SMART algorithm with 10 iterations was utilized. Correlation analysis was performed by the iterative multigrid algorithm with continuous shifting of interrogation boxes. The total number of iterations was four: two steps were performed with resolution 64×64×32 voxels and two extra iterations with a final resolution 32×32×16 voxels. The grid overlapping factor was selected equal to 50%. Therefore the final correlation domain size for calculation of a single velocity vector was 1.3×1.3×0.6 mm with half size distance between neighbor vectors. The final grid size was equal to 63×55×15 vectors. The average time of vector field reconstruction was equal to 180 s. Outlier detection rate was near 2%. Further the results obtained during data processing will be discussed. 5. Results and Discussion

(a) (b) (c) (d) Figure 2. (a) An instantaneous velocity field at time t and serial snapshots of spatial distributions of the Q criterion for (b) t, (c) t +∆t, (d) t +2∆t, time-resolved PIV measurements, ∆t = 6.4 ms, Re = 20 000.

Figure 2, (a) shows an instantaneous velocity field obtained by TR-PIV in the central section (z = 0) at an equal distance from the bounding surfaces. The figure presents a typical behavior for a quasi-two-dimensional jet. Based on the distribution of the velocity field, the flow can be divided into two distinct zones. The near zone extending from the nozzle exit to x/d = 3-4 is characterized by an intense entrainment of stagnant fluid into a stream, where the generation of coherent structures with the scale smaller than the depth h occurs. The far zone is the area of two-dimensional turbulence, which is located after x/d = 4 and characterized by the formation of large-scale vortices and the presence of the meandering effect with periodic deviation from the axis of a flow. The meandering stream is adjacent to large two-dimensional vortex structures with the opposite sign of rotation, which increases with expansion of the jet. Figures 2, (b)-(d) presents the distribution of positive values of the Q criterion calculated from the instant velocity fields in the section z = 0, obtained by a planar PIV for a sequence of frames. The time delay between the presented snapshots is 6.4 ms. This set of pictures shows the dynamics and

A1 A1

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mechanisms of vortex structures interaction. Due to limitations of spatial and temporal resolution we are unable to resolve the near field of the jet by TR-PIV.

(a) (b) (c)

(d) (e) (f) Figure 3. The spatial distribution of the normalized mean (a)-(c) streamwise velocity component and (d)-(e) crosswise velocity component for different z sections where (a), (d) refer to the central plane z/h = 0; (b), (e) – a plane between the central plane and the wall z/h = 0.25 and (c), (f) correspond to the closest plane to the wall z/h = 0.4. Results were obtained by planar PIV measurements. Re = 20 000. Taking into account the fact that the scale of vortex structures increases and the jet velocity decreases due to the influence of the bounding surfaces, we were able to explore the dynamics of large-scale structures and mechanisms of formation of these structures. In the sequence of fields with the Q criterion values calculated from the instant velocity fields it can be seen that starting from x/d = 5 vortex structures begin to interact with each other, forming the larger-scale structure consisting of two elements. Subsequently, these structures are combined into larger structures with the size by orders of magnitude greater than the depth of the channel. Letters Ai, Bi mark locations of the two selected vortex structures in the shear layer between the near and far zones of the jet. Figures 3, (a)-(c) present the spatial distribution of the mean streamwise velocity component in three different sections of the channel along the z direction. It can be seen that the flow in the central section (z = 0) is the jet flow with the distinct core and the linear expansion law of the jet. When approaching the measuring section closer to the wall (z/h = 0.25) the core of the jet narrows


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due to friction against the channel wall and the expansion law begins deviating from the linear law. Fields in Figure 3, (d)-(f) show the distribution of the mean radial velocity component in the same sections as distributions of streamwise velocity components. The distribution in the central section is characterized by the following picture. Near the nozzle up to x/d = 3 the jet does not expand. There is intensive fluid entrainment into the core of the jet and capture of fluid. For the section closer to the wall (z/h = 0.25) near the jet exit there is some difference with respect to the central section. Velocity in this section (z/h = 0.25) has the opposite direction than in the center plane. In the near-wall section (z/h = 0.4) the transverse velocity component changes its sign or direction of flow four times in a row. This variability of the mean radial velocity component dependence on the z coordinate indicates a complex three-dimensional flow structure and points to the fact that in the near field of the jet there are secondary flows.

(a) (b) Figure 4. (a) Comparison of the normalized mean velocity profiles obtained by planar Time-resolved PIV for axial and radial components, Tomo-PIV for all components; (b) a vector field of the mean velocity in the same cross-section of the flow, x/d = 3. Vector color denotes values of the radial mean velocity component, Re = 10 000.

(a) (b) Figure 5. (a) Comparison of the normalized profiles of axial and radial components of turbulent kinetic energy for different sections by the depth of the slot at x/d = 3, Re = 10 000. (b) Comparison between the inverse square of the axial normalized mean velocity component depending on the distance from the nozzle for different measurements. Figure 4, (a) presents the comparison of the profiles for normalized mean streamwise and radial velocity components given at the same locations for Tomo-PIV and TR-PIV results. The mean velocity field in the same cross-section of the jet is shown in Figure 4, (b) to explain the complex behavior of the profiles along the specified lines. The mean streamwise velocity components at the center plane obtained by planar and volumetric techniques show the agreement with relative velocity difference less than ten percent in the shear layer. The mean radial velocity component at the planar measurement plane z/h = 0.25 repeats

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qualitatively the result of Tomo-PIV measurements. A partial alignment could be explained by low accuracy of the mean radial velocity component estimate for current tomographic measurements which was at the level of 5% here and technical difficulties for the precise alignment of a thin laser sheet along the slot channel. The mean normal velocity component obtained by Tomo-PIV is also plotted here to demonstrate the potential of the volumetric technique. As for velocity fluctuations for axial and radial velocity components at the same sections through the depth of the slot they are plotted in Figure 5, (a). On the left hand side TR-PIV results have maximum values of fluctuations for the streamwise velocity component almost two times higher than Tomo-PIV results have. It could be linked with the different number of samples used for statistics 3000 and 500 and shorter time of evolution of the jet, which was 2.55 s for high speed measurements and near to 500 s for low repetition technique. Also there is a gradient along x direction within the shear layer for axial component of velocity fluctuations at x/d = 3 for both results. It might be estimated differently by TR-PIV and Tomo-PIV because of distinction in spatial resolution for xy plane which was close to four times. On the contrary fluctuations of the radial velocity component have comparable amplitude for both measurements and there is no significant gradient of radial velocity fluctuations to be observed in x direction here. It can be seen that the value of the turbulent intensity at the jet axis increases close to the wall due to developing of the turbulent boundary layer downstream and towards the central plane. Figure 5, (b) shows the inverse dependence of the square axial velocity normalized to the velocity at the nozzle exit obtained by the TR-PIV and Tomo-PIV. As one can see the data obtained by TR-PIV are in good agreement with data obtained by Tomo-PIV method. According to the scaling hypothesis, the dependence of the inverse square of the velocity should be a straight line. The figure shows the approximated data from the work Gordeyev and Thomas (2000), which correspond to the plane jet. As it was shown in the article Dracos et al. (1992), this dependence is determined by the depth h. If one reduces the depth h, the dependence starts to differ from the linear dependence. The authors of the work associated this distinction with the development of secondary flows in the near field of the jet and due to the direction of their movement. Fluid from the region of the jet, which has a high rate, is carried in the area of the bounding surfaces. At the same time the liquid with a slow speed outside the jet core is captured and sent to the central region. This effect leads to the decreasing of the jet velocity and thus leads to a deviation from linearity. Another factor that reduces the longitudinal velocity, and thus leads to a deviation from linearity is the development of the boundary layer, which begins to develop on the bounding surface and to grow out towards the central plane of the slot. During the analysis of Tomo-PIV results secondary flows were found in the shear layer of the slot jet. The mean structure of the flow in the near field of the jet is presented in Figure 6, (a) by cross-stream sections of the velocity magnitude. The streamwise velocity component decay along the jet axis and velocity gradients near the walls can be seen. Four counter rotating stationary vortices originating in shear layer near rectangular nozzle corners are also clearly visible. In Figure 6, (a) they are showed by isosurfaces of the streamwise vorticity component calculated for the mean velocity field. The length of the longitudinal vortices depends on the Reynolds number. They break up at 4d for Re = 10 000 and near 6d for Re = 20 000. Coherent structures with the vorticity normal to the wall of the slot cannot be seen at the mean velocity distribution due to their movement in streamwise direction. An attempt to visualize a structure of secondary flows by the instant volumetric velocity distribution in the near field region was done. However due to the low amplitude of the cross-stream instant velocity components with almost zero mean values and rms(v) = 0.57 voxels, rms(w) = 0.53 voxels throughout the volume characteristics based on the first velocity derivatives had a high noise level especially for the Q criterion. It should be stressed here that an amplitude of mean crosswise velocity components was 20-40 times lower compared to a centerline velocity


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values Uc~1.2 m/s which was equivalent to a shift of about 9 voxels. Thus maximum of V and W components have subpixel amplitude of about 0.2-0.4 voxels which is rather small and close to the accuracy limit of the Tomographic PIV measurements within 0.3 voxels (Atkinson et al., 2011). At these conditions an application of smoothing to the instant velocity fields leads to filtering low scale secondary flow structures as well as the measurement noise.

Figure 6. (a) Secondary flows in the near field by isosurfaces of the streamwise vorticity component calculated for mean velocity field, colored sections correspond to the mean velocity magnitude. (b) The streamwise vorticity component (blue and red) and Q criterion isosurfaces (yellow) for an instant velocity field reconstructed from ten most energetic modes of POD decomposition, Re = 10 000.

(a) (b) Figure 7. The comparison between (a) the measured instantaneous velocity distribution in the near field of the slot jet and (b) the reconstructed velocity distribution from first ten POD modes, the color map shows the streamwise velocity component, z/h = 0, Re = 10 000. A partial reconstruction of an instant velocity field from a limited number of POD modes helped to obtain the approximation that is suitable to visualize both the instant structure of longitudinal vortices and structures rotating normal to the wall. The POD decomposition could be used here as a correlation based low-pass filtering procedure from an ensemble of velocity fields. Figure 6, (b) demonstrates the result of this analysis. Here the blue and red isosurfaces denote longitudinal structures by wx and yellow isosurfaces correspond to the Q criterion. The relative rms error of the velocity magnitude for the whole 3D vector field between the origin and the reconstructed instant

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velocity field from first ten most energetic POD modes out of 500 was close to 30%, see Figure 7. From the analysis of the POD spectrum this limited number of modes contains near to 9% of turbulent kinetic energy. Single snapshot of a velocity field in Figure 6, (b) shows the possible mechanism of the longitudinal structures or secondary flows generation. The Kevin-Helmholtz instability in the shear layer induces vortices labeled by the yellow objects moving downstream. Due to wall friction and drifting velocity a vortex tube bends such that the velocity near the wall has the reversed direction to the entrainment velocity at the central plane (see Figure 4, b). That is vortex tube has two counter rotating tales or legs, colored by red and blue isosurfaces in Figure 6, (b) based on the opposite channel walls. The whole structure looks like a lambda structure in the turbulent boundary layer. As for the mean flow distribution the yellow vortex core disappeared by averaging its random positions from independent snapshots however the longitudinal vortex tails combined into long continuous structures visualized in Figure 6, (a). The spatial and temporal spectra of velocity fluctuations are presented in Figure 8 for both Tomo-PIV and planar TR-PIV measurements. They are typical for the two-dimensional turbulence. It was shown that with the development of large-scale vortex structures in the downstream direction, the maximum of the turbulent kinetic energy in the spectrum is shifted to longer wavelengths with a characteristic quasi-two-dimentional slope "-3". It is consistent with the results obtained by Dracos et al. 1992.

(a) (b) Figure 8. Spatial and temporal spectra of streamwise velocity fluctuations for Tomo-PIV and planar TR-PIV

measurements at different distances from the nozzle, Re = 20 000.

6. Conclusions Two modern optical measurement techniques Tomographic PIV and Time-resolved PIV were used to investigate the spatial-temporal flow structure of the turbulent slot jet. The data were acquired for the next flow regimes Re = {10 000, 20 000} by both applied techniques. Instant velocity derivatives, first and second statistical moments as well as spectral characteristics of the velocity fluctuations were shown and analyzed in this paper. For time-resolved measurements the behavior of vortices is examined in the middle and far zone of the jet by Q criterion. Coherent structures formed by the Kelvin-Helmholts instability in the shear layer turned into large quasi-two dimensional structures by pairing and deceleration of the jet with the bounding surfaces. Also planar PIV measurements indicate the presence three-dimensional structures in the near field of the slot jet due to altering of the radial velocity component for different depth sections. However their detailed visualization was not acquired because of low spatial resolution in the cross-stream direction with small number of sections and vectors. Clear secondary vortices in the near field of the slot jet were obtained by Tomo-PIV for the first time. On a mean spatial velocity distribution they look like longitudinal rolls within a shear layer beginning near the corners of the nozzle exit and spreading downstream up to 4d for Re = 10 000 and near 6d for Re = 20 000 close to the center plane.

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Direct quantitative comparison was done between planar Time-resolved PIV and Tomographic PIV measurements. Results of the mean streamwise velocity component show difference below 10% in the sear layer. The comparison for the mean radial velocity component and velocity fluctuations was only qualitative due to high relative error for this component and features of both experimental techniques. Acknowledgements The work was supported by AFDAR (#265695) project of 7th Framework Programme of EC, by program “Scientific and scientific-pedagogical personnel of innovative Russia for 2009−2013” of the Ministry of Education and Science of RF and by Russian Foundation for Basic Research project 12-08-00257-a. References Atkinson C., Coudert S., Foucaut J.-M., Stanislas M. (2011) The accuracy of tomographic particle image velocimetry for measurements of a turbulent boundary layer. Exp Fluids 50:1031–1056 Bilsky A.V., Dulin V.M., Markovich D.M., Shestakov M.V. (2007) Turbulence measurements in a quasi-two dimensional jet in a slot channel. Proc. of 5th International Symposium on Turbulence and Shear Flow Phenomena - (TSFP5), TU Munich, Germany, 27-29 August, 1067-1072 Bilsky A.V., Kaipov P.R., Markovich D.M., Tokarev M.P. (2005) Application of Proper Orthogonal Decomposition (POD) to the analysis of velocity fields in turbulent impinging jet flow. Proc. of 6th International Symposium on Particle Image Velocimetry, Pasadena, California, USA, 21-23 September Bilsky A.V., Lozhkin V.A., Markovich D.M., Tokarev M.P. (2012) Maximum Entropy Reconstruction Technique for Tomographic Particle Image Velocimetry. Proc. of 16th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal, 9–12 July Dracos T., Giger M. and Jirka G.H. (1992) Plane Turbulent Jets in a Bounded Fluid Layer J of Fluid Mech 241:587–614 Gorin A.V., Sikovsky D.Ph., Nakoryakov V.E., Zhak V.D. (1998) Two-dimensional turbulent jet in a hele-shaw cell. Proc. 7th International Symposium on Flow Modeling and Turbulence Measurements. Tainan, Taiwan: 269-279 Foss J. F., Jones J. B. (1968) Secondary flow effects in a bounded rectangular jet Trans ASME, J. of Basic Eng :241 – 248 Gordeyev S.V., Thomas F.O. (2000) Coherent structure in the turbulent planar jet. Part 1. Extraction of proper orthogonal decomposition eigenmodes and their self-similarity J Fluid Mech 414:145-194 Heskestad G. (1965) Hot-wire measurements in a plane turbulent jet Trans ASME, J of Appl Mech :721 – 734 Khashehchi M., Elsinga G.E., Ooi A., Soria J. (2010) Studying invariants of the velocity gradient tensor of a round turbulent jet across the turbulent/nonturbulent interface using Tomo-PIV. Proc. of 15th international symposium on applications of laser techniques to fluid mechanics, Lisbon, Portugal, 5–8 July, 2010 Owczarek J.A., and Rockwell D.O. (1972) An experimental study of flows in planar nozzles. - Mechanism of the secondary flow. Trans ASME, J of Basic Eng 94: 682 – 687 Schröder A., Geisler R., Elsinga G.E., Scarano F., Dierksheide U. (2008) Investigation of a turbulent spot and a tripped turbulent boundary layer flow using time-resolved tomographic PIV. Exp Fluids 44: 305-316 Violato D., Scarano F. (2011) Three-dimensional evolution of flow structures in transitional circular and chevron jets. Phys Fluids 23, 124104

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