Time Resolved Stereoscopic PIV measurements in the near ...ltces.dem.ist.utl.pt/lxlaser/lxlaser2008/papers/09.3_3.pdf · Time Resolved Stereoscopic PIV measurements in the near wake

14th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2008

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Time Resolved Stereoscopic PIV measurements in the near wake of a circular

cylinder at high Reynolds number

R. Perrin1, M. Braza2, E. Cid2, S. Cazin2, F. Thiele3, J. Borée1

1: Laboratoire d’Etude Aérodynamique (LEA), Université de Poitiers, ENSMA, CNRS SP2MI, téléport 2 Bd Marie et Pierre Curie, 86962 Futuroscope Chasseneuil, France

2: Institut de Mécanique des Fluides de Toulouse, allée du pr. Camille Soula, 31400 Toulouse, France 3: ISTA, T. U. Berlin, Sekr. HF1, Mueller Breslau Str. 8 D-10623 Berlin Germany

Abstract This study is complementary to a precedent one in which the very near wake of a cylinder was experimentally studied with the goal of providing a physical analysis of the coherent and turbulent motions in the near wake, and a database as useful as possible for improvement and validation of turbulence modeling. The flow is investigated using TRPIV and 3C-TRPIV in plans of different orientations in the near wake. The main goal of the present study is to complete a previous analysis of the von Kármán vortices, which was achieved using POD and phase averaging, by analysing the longitudinal vortices which connect the primary ones. To this aim, Time Resolved 2C-measurements have been carried out in a (x, y) plan orthogonal to the cylinder, allowing the study of the primary von Kármán vortices, and Time Resolved 3C measurements have been carried out in (x, z) plans along the span, allowing the analysis of the longitudinal vortices. Two tasks are necessary for the analysis. The first one is to recognize and characterize longitudinal vortices in the (x, z) plans. This is done using the technique developed by Schram et al, based on a wavelet analysis of the enstrophy. The second task is to characterise these vortices with respect to the von Kármán vortices. It is therefore necessary to relate the fields in the (x, z) plans to the field in the (x, y) plan. In a first step, this is done by estimating the phase averaged field from the velocity field on the center line intersecting the plans. This allows a description of the longitudinal vortices according to the shedding phase angle, and with respect to a ‘mean’ von Kármán vortex street. As it has been observed that the shedding becomes irregular during short periods of time appearing randomly, it is attempted in a second step to reconstruct part of the instantaneous flow from the mean center line velocity. This is done using Extended POD, introduced by Borée, 2003. Statistics are then performed on the detected longitudinal vortices according to the phase of the shedding and a mean picture of the coherent motion is obtained in the near wake region.

1. Introduction A considerable number of studies have been devoted to the flow past a circular cylinder and have shown that this flow is characterised by the birth of coherent structures at low Reynolds number and by their persistence at high Reynolds numbers in the turbulent regime. The main structures are the von Kármán shedding, generated by a global instability, and which has been studied by many authors (e.g. Cantwell & Coles, 1983 , Hussain & Hayakawa, 1987,…), the longitudinal vortices that connect the primary ones, and which result from a secondary instability (e. g. Williamsson, 1992, Persillon & Braza, 1998, Hayakawa & Hussain, 1989, …), and the smaller scales Kelvin Helmoltz vortices, which result from a convective instability in the shear layer (e.g. Bloor,1964, Kourta, 1987, Braza & al, 1990, …). Numerical simulations of this class of detached unsteady flows past bluff bodies, remains very challenging, especially because of this dual character of the flow, with organised and turbulent motions superimposed and interacting non linearly. Therefore, an experimental data base allowing validation and enhancement of turbulence modeling for this class of flow is of significant relevance. At high Reynolds numbers, while URANS type simulations results, in most of the cases, in the prediction of the von Kármán vortices, recent efforts have been devoted to hybrid approaches (e. g. DES, PITM …) which aim at combining the respective advantages of RANS and LES. These kinds


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of simulations typically lead to a RANS behavior near the walls and to a LES behavior in the separated regions. Therefore, recent simulations are able to resolve more and more details of the fluctuating motion, and it is necessary, for validation purpose, to furnish details about structures in the fluctuating motion. The present study aims at providing a physical analysis of the coherent and turbulent motion in the near wake of a cylinder and a data base useful for validation of turbulence modeling. To avoid uncertainties related to ‘infinite conditions’ usually occurring when one compares a simulation to an experiment, the cylinder was placed in a channel with a high blockage coefficient and a low aspect ratio. In previous studies, the von Kármán vortices were analysed using POD and phase averaging, carried out on PIV measurements in the mid span plan orthogonal to the cylinder. The achieved data base consisted in mean velocities and turbulent quantities (e.g. turbulent stresses, production terms…) in a phase averaged sense. This data base can be used for validation purpose, either by comparing directly the phase averaged motion and turbulent quantities in the case of a URANS type simulation, or by applying the same processing as for the experiment, in the case of a LES or hybrid simulation (e. g. Perrin, 2007). However, it is worth characterising the three dimensionality of the flow, especially the secondary longitudinal vortices connecting the primary von Kármán ones. To this end, Stereoscopic Time Resolved PIV (3C-TRPIV) was performed in different plans in the near wake, oriented parallel to the cylinder axis ((x, z) plans), and 2C-TRPIV was performed in a plan orthogonal to the cylinder ((x, y) plan). The experimental set-up is discussed in section 2. Two tasks are necessary to characterise the longitudinal vortices with respect to the von Kármán ones. The first step is to identify the vortices in the plans parallel to the cylinder. This is done using the technique introduced by Schram & al, 2004, based on a wavelet analysis of the enstrophy, as described in section 3. The second task is to relate the detected vortices to the von Kármán shedding. To this end, the motion in the (x, y) plan is reconstructed at each instant of acquisition of the (x, z) plans, firstly using phase averaging in section 4.1, and then using Extended POD, introduced by Borée, 2003, in section 4.2.

2. Configuration and experimental set-up

Measurements have been carried out in the closed wind tunnel S4 of IMFT (Fig. 1), of cross section H x L = 61 x 71cm2. The cylinder of diameter 12.5 cm was mounted on the walls, spanning the height of the channel, without end plates. This results in a blockage coefficient of D/H=0.21, and an aspect ratio of L/D=5.7. As explained in the previous section, this highly confined environment was chosen to allow computations to be performed on a domain of restricted size, and with no ambiguity on the boundary conditions. The upstream velocity U0 was 16.8 m/s, resulting in a Reynolds number of 140,000. In the following of the paper, x, y and z denotes the longitudinal, transverse and spanwise directions, respectively, and the origin is located at the centre of the cylinder. U, V and W denotes the velocity components along these directions. All quantities have been non-dimensionalised using U0 and D. In a first step, 2C-TRPIV measurements have been carried out in a (x, y) plan orthogonal to the cylinder axis, as represented in Fig. 2. Measurements were carried out using a laser Darwin 2x20mJ from Excel Technology, a camera CMOS APX (PHOTRON) with a resolution of 1024x1024 pixels, and DEHS as seeding particles (typical size 1µm). The system allowed acquisitions of image pairs at a rate of 1 kHz. The image pairs were analysed using an in-house code ‘PIVIS’ developed by the ‘Service Signaux Images’ of IMFT, which uses an algorithm based on a 2D FFT cross correlation function implemented in an iterative scheme with a sub-pixel image deformation (Lecordier & Trinite, 2003). The flow was analysed using 50% overlapping windows of 32 x 32 pixels, yielding fields of 61 x 57 vectors with a spatial resolution of 3 mm (0.0238 D). Approximately 2% of the calculated vectors were detected as outliers using a sort based on the norm, the signal-to-noise ratio, and a median test filter, and these vectors have been replaced using a second order least-square interpolation scheme. Four temporal series of 3072 images pairs were


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analysed, each series containing roughly 85 shedding periods.

Fig. 1. S4 Wind tunnel and configuration for the

3C-TRPIV measurements Fig. 2. Different plans of measurements

Stereoscopic Time Resolved PIV was performed in (x, z) plans in the near wake. This was achieved using a Pegasus laser from New Wave delivering 2x10mJ, operating at 1kHz, and two CMOS cameras RS3000 (Photron) with a resolution of 1024x1024 pixels, used in Scheimpflug angular configuration, and equipped with two 85 mm Nikon lens at f# = 2. The so-called pinhole-based model was considered (Tsai, 1987). In order to retrieve external and internal parameters of both cameras, a planar calibration target with dots was positioned by hand (Heikkil, 2000, Zhang, 1999). Calibration was performed using 8 images of different positions of the target (Wieneke, 2005). Concerning the precision of the dot images detection, as in a previous study (Perrin & al, 2007), a reconstructed mean dot is correlated with real images. The standard deviation error of dot position was found less than 0.08 pixel. A disparity correction scheme, on PIV images, enabled to account for misalignment between reference target position and laser sheet (Perrin & al, 2007). Vector fields were calculated from the images pairs in the same manner as for the 2C-measurements. These measurements have been carried out in plans at y/D=0 and y/D=-0.4 (Fig. 2). The mean resolution in these plans is 2 mm (0.015D). The same detection of outliers and replacements by interpolation as for the 2C fields has been performed. The data set consists in 12 series of 3072 fields acquired at 1 kHz for each plan.

Fig. 3. Correlation uw and vw in the plan y/D=0 (3C-TRPIV)

Fig. 4. Spectra of u and v velocity at x/D=1.33, y/D=0, z/D=0 from (x, y) and (x, z) plans.

As the flow is found statistically homogeneous on a large part of the cylinder span, the

correlation uw and vw have to be null. As the calibration has a strong influence on these quantities, it is checked on Fig. 3 that low values are obtained. Comparisons between the measurements in each plan have also been made and a good agreement was found. Fig 4 shows the spectral contents of the velocity at a point common to 2C-TRPIV and 3C-TRPIV measurements plan at y/D=0.


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3. Identification of the vortices

To identify the longitudinal vortices in the (x, z) plans, the technique introduced by Schram & al (2004) have been used. It is based on a continuous wavelet analysis (Farge, 1992) of the enstrophy (squared vorticity ω2). The mother wavelet is the Mexican hat which is written:

)2

exp()2(),(22

22 zxzxzx

+−−−=Ψ

For one snapshot, the wavelet transform of the enstrophy field is then obtained by the convolution product:

∫ Ψ= '')','()','(),( ,,2 dzdxzxzxzxC yxll ω where )

2

)'()'(exp(

)'()'(2

1)','(

2

22

2

22

,,l

zzxx

l

zzxx

lzxyxl

−−−−

−−−−=Ψ

a) in the plan y/D=0

b) in the plan y/D=0.4

Fig. 5. Typical structure detection

The local maxima of the three dimensional scalar field ),( zxC l indicates the presence of a patch

of vorticity and then possibly a vortex at the position (x, z). As demonstrated by Schram & al, the length scale l at which the maximum is found can be related to the diameter of an Oseen vortex (D=2.5886l), and hence gives an indication on the size of the detected structure. To enhance


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detection and to reject patches of vorticity associated with a shear motion, or with two small vortices which are merging, the fluctuating velocity field in the region indicated by the wavelet analysis is correlated with the velocity field corresponding to an Oseen vortex of the diameter deduced from l. A threshold is then applied on the correlation and the parameters x, z and l of the structures having a correlation coefficient higher than 0.85 are stored. A limitation of this technique is the isotropy of the wavelet used for the identification, while the pattern of a vortex in a plane cutting the 3D field is not necessarily circular. Particularly in our case, we do not expect the axis of the vortices to be orthogonal to the measurement plans and therefore the pattern of the vortices would have a priori more an elliptic shape than a circular one. Therefore, it is more appropriate to consider the procedure above as a detection method than as an eduction method. To educe a typical shape of the detected vortices, one possibility is be to ensemble average the instantaneous velocities associated with each detected vortices found at one given location and phase of the shedding. This operation will be performed in the next section. Fig. 5 shows typical vortices detected by the algorithm described above in the plans y/D=0 and y/D=-0.4. Several observations can be made. In both plans, the detection algorithm is able to identify pairs of counter-rotating vortices (Fig. 5a and 5b left), a pattern that in agreement with many other studies (e. g. Hayakawa & Hussain, 1989, Sung & Yoo, 2001). It is also confirmed that the detected vortices do not have necessarily a circular shape. The algorithm also detects smaller structures which are attributed to the random turbulent motion and which do not seem to present any degree of organisation (Fig. 5 a and b, right). The large range of scales detected by the algorithm is confirmed by the histogram of the diameters shown in Fig. 6a. In the next sections, a threshold will therefore be added before ensemble averaging. Fig. 6b shows a histogram of the core circulation of the detected vortices, and it is observed that vortices of both signs are found with a similar probability, as expected.

Fig. 6. Histograms of the size (left) and of the core circulation (right) of the detected vortices

4. Reconstruction of the flow

To characterise the longitudinal vortices, it is necessary to relate their evolution to the von Kármán shedding. As the (x, y) plan and the (x, z) plans have been acquired independently, it is necessary to estimate the flow in the (x, y) plan at each instant of acquisition in the (x, z) plans, or at least, to evaluate the phase of the shedding. The first part of this section attempts to evaluate the phase averaged motion, and to educe a typical pattern of the longitudinal vortices, according to the phase of the shedding. It has also been shown in previous studies that the shedding becomes irregular during short periods of time occurring randomly. It is therefore attempted in the second part to estimate part of the instantaneous flow.


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4.1 Phase averaged flow In different studies, it has been shown that the phase of the shedding can be evaluated directly using the velocity field itself, rather than using an external trigger signal, as the wall pressure on the cylinder or a hotwire signal on the side of the wake. One possibility is to observe that the two first coefficients of a POD performed in a plan in the wake have a quasi sinusoidal evolution, both being shifted by a quarter of period. It is therefore possible to define a phase angle directly from these coefficients. In Perrin & al, 2007, it has been shown that the phase averaged motion was also better captured using this technique than when using a pressure signal, because the vortices are less smoothed by a cycle-to-cycle variation of their position. This leads to consider using directly the velocity on the line intersecting the (x, y) and (x, z) plans, to define the shedding phase angle. A similar technique to that used in Perrin & al, 2007 have been applied, except that time delays are also considered in the POD. Considering a time window of length 30/fs, which corresponds to approximately one shedding period, one snapshot is constructed using the velocity fluctuations u and v on the axis common to the (x, y) plan and the considered (x, z) plan during this time window. Therefore, in the POD, both space and time correlations are considered. Considering such time delays is similar to the technique used by Debesse & al, 2006, based on a SVD of the delays matrix of a time serie, introduced by Broomhead & King, 1986. Taking into account time delays is necessary in this case because a classical POD would result in very noisy modes and coefficients because of the restricted size of the domain (a line) considered. Once this POD is performed, the coefficients associated with the two first POD modes, which are plotted in Fig. 7 and which present a quasi sinusoidal evolution, can be used to define a phase angle representative of the shedding, in the same way as in Perrin & al, 2007. Using this phase angle, the phase averaged motion is then estimated using LSE, as in Perrin & al 2007b. It is noticeable that at some instants occurring randomly, the shedding becomes irregular. These instants cannot be taken into account for the estimation of the phase averaged motion. It has also been observed that during these instants, the amplitude of the first two POD coefficients used for the determination of the phase, decrease toward zero. Therefore, a threshold is applied on the amplitude of the coefficients, and the corresponding irregular periods are rejected during the estimation of the phase averaged motion. One important thing to check, is the ability to estimate the same phase angle and then reconstruct the same phase averaged flow from the plan y/D=0 and from the plan y/D=-0.4. Tests have been performed using velocities extracted from the (x, y) plan measurement at the (x, z) plans locations. While a mean phase shift has to be added to the phase angle deduced from the line y/D=-0.4 to superimpose it with the angle deduced from the line y/D=0, it can be seen in figure 7a that a very good agreement is achieved. Consequently, the phase averaged motions estimated from both lines are very close, as can be observed in figure 7b.

a) top: first two coefficients of the POD with time delays (plan y/D=0); bottom: phase angle determined from line y/D=0 and y/D=-0.4

b) Phase averaged motion evaluated from both lines: Ω21

component evaluated from y/D=0 line (red dashed line) and y/D=-0.4 (blue solid line) at phase angle 135°.

Fig. 7 Phase averaging


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Once the phase averaged motion have been estimated using the (x, y) plan, the same procedure can be applied to the data extracted from the (x, z) data on the same lines, to determine the shedding phase angle and then the phase averaged motion at the instants of acquisition of the (x, z) plans. Fig.8 shows pictures extracted from movies where both the instantaneous motion in the (x, z) plan (at y/D=0) and the estimated phase averaged motion in the (x, y) plan are represented, and which allow to locate the structure detected in the (x, z) plan with respect to the von Kármán vortices. In addition to the tests performed in the (x, y) plan, visual inspections of the velocity vectors shows that the reconstruction from the (x, z) plan measurements appears satisfactory. In the example of instantaneous flow represented in these figures, traces of longitudinal vortices in the (x, z) plans appears located between the main von Kármán vortices. To evaluate the most probable position of the detected vortices in (x, z) plans, the number of detected vortices has been plotted as a function of the shedding phase angle and the x/D position for each plan in Fig. 9. It is observed that the most probable position of vortices is a function of the shedding phase angle and this position is located between two von Kármán vortices. This is consistent with the accepted scheme of longitudinal vortices located near saddle points between the von Kármán vortices and aligned with their separatrix. It is also observed that two maxima occur in the histogram of Fig. 9 during a period in the plan y/D=0. This is coherent with the symmetries of the flow with respect to the y/D=0 axis for two opposite shedding phase angles.

(x, z) plan at y/D=0 (x, z) plan at y/D=-0.4

Fig. 8 Instantaneous flow in the (x, z) plane and estimated phase averaged field in the (x, y) plane

(x, z) plan at y/D=0 (x, z) plan at y/D=-0.4 Fig. 9 number of detected vortices versus phase angle and x position


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Having established a most probable x position of the detected vortices at a given phase angle, it is worth trying to conditionally average these vortices to obtain a typical pattern of longitudinal vortices. Different parameters have to be chosen for these conditional averaging. As the flow is not stationary, and is not homogeneous in x direction, different classes have been defined according to the phase angle and to the x position of the detected vortices. Also, as a large range of size of vortices was detected, classes were also defined according to the size. One period was divided into 16 intervals of width 2π/16. In each interval, an interval of width 0.06D centered around the corresponding most probable x location of vortices was considered. The velocity associated with all detected vortices falling into this classes and having a size between 0.1D and 0.2D were averaged, depending also on the sign of their circulation. As the flow is homogeneous in z direction, the instantaneous fields were shifted in z, to place the center of the vortices at z/D=0. Averaging is then performed with approximately 200 fields per classes. Fig. 10 and 11 presents the averaged velocities and vorticity in both plans at the phase angle 214°, for negative and positive circulation, respectively. It can be first observed that the positive and negative averaged vortices are rather similar, owing to the vorticity and the velocity field. This is coherent with the observed symmetry in the histogram of the circulation (Fig. 6b). As already observed in Fig. 9, the position of the mean vortex is x/D~1.4 in the plan y/D= -0.4 and x/D~1.05 in the plan y/D= 0, which suggests an alignment of the detected structures with the separatrix of the saddle point, between the main von Kármán vortices. The topology of the v velocity component (normal to the plane), which is increased on the side z>0 and decreased on the side z<0 for the negative vortex (and oppositely for the positive vortex) is also in agreement with this orientation of the vortices.

Ω31 and velocities (u, w): y/D=0 plan Ω31 and velocities (u, w): y/D=-0.4 plan

Velocities v (contours) u, w (vectors): y/D=0 plan Velocities v(contours) , u, w (vectors): y/D=-0.4 plan

Fig. 10 Conditionally averaged negative vortices in both (x, z) plans at phase angle 214°

Although the averaging was performed in both plans using the same class of size, it seems also that the extent of vorticity is slightly larger in the y/D=-0.4 plan. Finally, the velocity fields in the y/D=-0.4 plan seems to show another vortex of opposite sign on the side of the main one (at z/D~-


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0.3 for the negative vortex and at z/D~0.3 for the positive vortex). This let suppose the existence of pairs of vortices which would be in agreement with many studies (e.g. Hayakawa & Hussain 1989, Sung & al 2001). However this vortex is highly smoothed in the averaging procedure because of a significant jitter. Visual inspection of the instantaneous fields shows large variations of positions and orientations of the observed pairs of vortices. Similarly, although pairs of vortices have been observed in the y/D=0 plan, this is not reflected in the averaged result. An explanation is that the flow is far more chaotic in the center of the wake than on its side, and that the jitter is too important there to obtain pairs of vortices in the y/D=0 plan using a detection based on only one vortex.

Ω31 and velocities (u, w): y/D=0 plan Ω31 and velocities (u, w): y/D=-0.4 plan

Velocities v (contours) u, w (vectors): y/D=0 plan Velocities v(contours) , u, w (vectors): y/D=-0.4 plan

Fig. 11 Conditionally averaged negative vortices in both (x, z) plans at phase angle 214°

4.2 Instantaneous flow

The reconstruction achieved by phase averaging allows determining a mean position and shape of the vortices with respect to the von Kármán vortices. However, it has been shown that the shedding can become irregular during short periods of time. Also the strong jitter observed in the preceding section, leads to consider reconstructing the significant part of the fluctuating motion in the (x, y) plan, to be able to analyse instantaneous snapshots. This last section deals with such a reconstruction using Extended POD, introduced by Borée, 2003. The present application of EPOD uses the fluctuating velocities u and v on the line common the (x, y) and (x, z) plan, during a time window of length 30/fs. POD is then performed and each mode can be extended using the instantaneous fields in the whole (x, y) fields. The flow can then be reconstructed using the coefficient associated with the POD mode and the corresponding extended modes. Borée, 2003 has demonstrated the equivalence with LSE, when one considers all POD modes. Before applying EPOD to the (x, z) measurements, the extended modes have been determined using the (x, y) data and the reconstruction have been compared to the instantaneous fields. The velocities used for the POD are extracted from the line y/D=0. Although not shown here, the first three extended modes


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obtained in this way are very similar to the first three modes that would be obtained by performing a POD on the whole field. Figure 12 shows examples of reconstructed velocities. Fig. 12a shows the time evolution of u and v at a point in the wake together with the estimated u and v using 3 and 20 modes. A very good agreement is achieved, and it can be seen that the reconstruction is also satisfactory at the instants when the shedding is less regular, when the periodic component deteriorates. Fig. 12b, c and d present an instantaneous field of vorticity and the corresponding reconstructed fields using 3 and 20 modes. It can be seen that a good agreement is also obtained, the reconstruction being more precise using 20 modes, as expected. Considering the ensemble of the fields, approximately 56% and 67% of the fluctuating energy on the domain is reconstructed using 3 modes and 20 modes, respectively.

a) b)

c) d) Fig. 12 Extended POD in the (x, y) plan using the velocity on the line y/D=0;

a) time series of u and v velocities at x/D=1.2 and y/D=0.25, and estimated u and v using 3 extended modes (blue) and 20 extended modes (red);

b), c) and d) instantaneous field of vorticity and estimated field using 3 (c) and 20 modes (d). Finally, once the extended modes have been determined, the velocities extracted on the common line from the (x, z) plan can be used to estimate the POD coefficients at each instants of acquisition in the (x, z) plan (by projection onto the POD modes) and then to estimate the velocities in the (x, y) plan. Two examples of reconstruction are plotted in Fig. 13. The snapshot in Fig 13a is taken at an instant where the shedding is regular while the instant represented in Fig 13b corresponds to a period of irregular shedding. During the time of irregular shedding, two quasi stationary lobes of


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vorticity are observed on each side of the wake in the (x, y) plan and the instantaneous flow in the (x, z) plan seems dominated by a recirculating flow with small scale fluctuations, and no dominant structure have been observed.

a) b) Fig. 13. Reconstruction of the flow in the (x, y) plan using EPOD and (x, z) measurements at y/D=0. 5. Conclusion and perspectives

The flow past a circular cylinder at Reynolds 140,000 has been experimentally studies, with the main goal of providing details on the structures arising in the wake, in complement to a precedent study where the von Kármán vortices were analysed. In particular the three dimensionality of the flow was investigated and it was attempted to characterise the longitudinal vortices connecting the primary ones at this high Reynolds number. 3C-TRPIV in (x, z) plans were carried out and the data have been analysed using a wavelets analysis of the enstrophy in these plans. Furthermore, an estimation of the motion in a (x, y) plan at each instants of acquisition, using phase averaging and then Extended POD has allowed to study these vortices with respect to the main von Kármán vortices. A mean pattern of the longitudinal vortices have been deduced. It has also been observed that vortices appears often by pairs, in agreement with other studies, but large variations in the position of these vortices at given shedding phase angle leads to difficulties for educing these pairs using a detection based on one vortex. A future study should be devoted to the identification of pairs of counter-rotating vortices, using an adapted pattern recognition technique. Acknowledgements The authors acknowledge the partial funding of the work presented here by the European Community during the DESider project (Contract No AST3-CT-2003-502842), and by the German Research Foundation (DFG) within the scope of the collaborative Reserche Center SFB 557.

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Time Resolved Stereoscopic PIV measurements in the near ...ltces.dem.ist.utl.pt/lxlaser/lxlaser2008/papers/09.3_3.pdf · Time Resolved Stereoscopic PIV measurements in the near wake