9TH. INTERNATIONAL SYMPOSIUM ON FLOW VISUALIZATION, 2000
Improve the Spatial Resolution of PIV Results by
Using Hierarchical Recursive Operation
Hui HU, Tetsuo SAGA, Toshio KOBAYASHI
Nobuyuki TANIGUCHI and Shigeki SEGAWA
Keywords: PIV technique, spatial resolution of PIV results, hierarchical recursive PIV,
multiple correlation validation technique, jet mixing flow
ABSTARCT
An improved PIV image processing algorithm named as Hierarchical Recursive PIV (HR-PIV)
method, which can get a very high spatial resolution compared with conventional PIV image
processing methods, was described in the present paper. By starting with a large interrogation
window size and search distance as the same as conventional correlation analysis based PIV image
processing methods, HR-PIV method improves the spatial resolution of PIV results through
hierarchical reduction of the interrogation window size and search distance by using the results of
former iteration step. In order to suppress the appearance of spurious velocity vectors, Multiple
Correlation Validation technique was used to improve the Signal to Noise Ratio (SNR) level of the
correlation table as the interrogation window size hierarchically decreasing. A new overlap
arrangement of neighboring interrogation windows for the Multiple Correlation Validation
technique was also proposed in the present paper, which can insure the same spatial resolution
level in X and Y axial direction. In order to demonstrate the effect of the spatial resolution level of
PIV results on the small-scale vortex identification capability, HR-PIV method with Multiple
Correlation Validation (MCV) technique was used to do PIV imaging processing for jet mixing
flows. The PIV results from the same PIV images at different spatial resolution levels were
compared qualitatively and quantitatively. It was found that more and more small-scale vortices
and turbulence structures, which can not be identified by using conventional PIV image processing
methods, could be revealed successfully in the velocity vector fields by using the present HR-PIV
method as the spatial resolution level of PIV results increasing.
1. Introduction
As a modern optical flow field measuring technique, Particle Image Velocimetry (PIV) can offer
many advantages for the study of fluid flow over other conventional one-point measurement
techniques like Laser Doppler Velocimetry (LDV) or Hot Wire Anemometer (HWA). PIV
technique can measure the velocity of whole two-dimensional or three-dimensional flow field
instantaneously without disturbing to reveal the global structures of a complicated and/or unsteady
flow field quantitatively. So it was widely used and rapidly developed in the past two decades.
Although much progress had been made in improving the accuracy and the processing speed of
PIV technique, there is still the possibility of improvement in several aspects of this technique, as
the technologies related PIV image acquisition and image processing. Two major problems can be
identified with current image processing techniques related to PIV are (1). Limitation on spatial
Author(s):
Institute of Industrial Science, University of Tokyo
Roppongi 7-22-1, Minato-Ku, Tokyo 106-8558, Japan
Corresponding author:
Email:
Paper number 137
Hui HU
huhui@iis.u-tokyo.ac.jp
137-1
Hui HU, Tetsuo SAGA, Toshio KOBAYASHI, Nobuyuki TANIGUCHI and Shigeki SEGAWA
resolution of the estimated displacement field. (2). Limitation on the dynamic range of
displacements (i.e., the difference between the largest and smallest displacement) that can be
accurately measured. These two problems are in fact related and complementary.
In the current stage, the most widely used methods for PIV image processing can be fall into two
categories, i.e., the particle tracking methods and spatial correlation analysis methods (including
auto-correlation method or cross-correlation method) (Figure 1.). The particle tracking methods are
based on the tracking of individual particles with the time sequence, and vectors are obtained at
random points in space. Since most of the particles tracking algorithms rely on the assumption that
nearest neighbouring images belong to the same particles, and this is not valid if the particle image
density becomes too high. So, the particle tracking methods are normally limited to relatively low
particle image density. Hence, it always provides poor spatial resolution. Although Keane et al. [1]
had proposed a “super-resolution PIV method” by coupling particle tracking technology with
spatial correlation method, which can expand the application range of particle tracking method to
relatively high particle image density. However, such method will be invalid for extremely high
particle image density where the particle overlap, agglomeration, diffraction and distortion of the
light may prevent the use of particle tracking technology.
Rather than tracking individual particles, the spatial correlation analysis methods are used to
obtain the average displacement of the ensemble particles. The recorded PIV images were divided
into many smaller sub-regions (which are called interrogation windows). Each interrogation
window contains several particle images. Analysis of the displacement of images in each
interrogation window by means of spatial correlation operation (either cross-correlation or autocorrelation method) leads to an estimated average displacement of particles included in the
interrogation window. This approach is valid for the case in which many particle images were
included in per interrogation window, referred to as the high image density limit (Adrian, [2])
By using spatial correlation method, the obtained velocity vector is actually the spatially
averaged velocity of the particles included in each interrogation window. The spatial resolution of
the PIV results can be achieved is directly related to the size of the interrogation windows. The
displacement vector computed at any location is the spatially averaged “transitional” motion of
particles in the interrogation window, any information on the velocity fluctuations and the
rotational component of the velocity field within the region of the flows covered by the
interrogation windows is lost in the computational process. Therefore, the vortices with their scale
less than interrogation window size always can not be revealed successfully from the PIV result. In
order to reveal the small-scale vortices in the flow field, the interrogation window size should be
reduced as small as possible.
Search region for time step t=t3
Searching window
Search region for
time step t=t4
Interrogation window
Search region for time step t=t2
Particle position of time step t=t1
a. Particle tracking method
b. Spatial correlation based PIV image processing method
Figure 1. Two kinds of common used PIV image processing methods
9th International Symposium on Flow Visualization, Heriot-Watt University, Edinburgh, 2000
Editors G M Carlomagno and I Grant.
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IMPROVE THE SPATIAL RESOLUTION OF PIV RESULT BY USING HIERARCHICAL
RECURSIVE OPERATION
However, according to the research of Keane and Adrian. [3], at less ten-tracer particle images
per interrogation window should be satisfied in order to resolve the local particle displacement
accurately by using the conventional correlation analysis based image-processing algorithms. Hu et
al. [4] had also suggested that the optimum particle number in an interrogation window be about
10-20 for the cross-correlation method. These indicate that interrogation window size should be big
enough to contain sufficient number of particle images to insure a high probability of uniqueness of
the solution by using conventional correlation based PIV image processing methods.
If a prior information of the local displacement is known, even by using a smaller interrogation
window can get the statistically meaningful results. This is the basis of the Hierarchical Recursive
PIV method (HR-PIV) to be introduced in the present paper. Hierarchical Recursive PIV operation
is actually a hierarchical recursive process of conventional spatial correlation method with
offsetting of the displacement estimated from the former iteration results and hierarchical reduction
of the interrogation window size and search distance in the next step (Figure 2). As the
interrogation window size decreasing hierarchically, the spatial resolution of the PIV result
increased substantially.
Level 1
Level 2
Level 3
a. The principle of the Hierarchical Recursive PIV method
Offset
Velocity vector at coarse grid level
velocity
Velocity vector at refined grid
Vector obtained at new calculation loop
b. Operation steps
Figure 2. The schamatic of the present Hierarchical Recursive PIV method
9th International Symposium on Flow Visualization, Heriot-Watt University, Edinburgh, 2000
Editors G M Carlomagno and I Grant.
137-3
Hui HU, Tetsuo SAGA, Toshio KOBAYASHI, Nobuyuki TANIGUCHI and Shigeki SEGAWA
2. The operation steps of Hierarchical Recursive PIV (HR-PIV) method
Hierarchical Recursive PIV operation steps may be expressed as following:
Step 1:
Conduct a normal correlation operation with big interrogation window size and
big research distance, which is as the same as conventional correlation based
PIV image processing methods.
Step 2:
Scan for spurious vectors and replace the spurious vectors by interpolation
(Kimura et al. [5] and Westweel [6]). Since the obtained displacements serve as
only the estimate for the next finer resolution level, and the error in the upper
level may propagate down to the smallest scale, so the spurious vector detection
criterion can be more stringent than conventional correlation PIV methods. Data
smoothing may also be used.
Step 3:
Project the estimated displacement data to the next finer spatial resolution level.
Use these displacement data to be the offset of the interrogation windows in the
next step (Figure. 2).
Step 4:
Conduct a new correlation operation with smaller interrogation size. The
smaller search distance can also be deduced based on the velocity gradients
estimated from the displacements at the former coarse level (Keane et al. [1]).
Step 5:
Repeat the step 2 to step 4 until the desired spatial resolution level is obtained.
Step 6:
Finally perform a spatial correlation operation at the desired interrogation
windows size without outliner removal and smoothing treatment, sub-pixel
interpolation (Hu et al. [4]) should also be conducted to improve the accuracy of
the PIV result.
It was well known that, as the interrogation window size decreasing, the particle image number
included in the interrogation window decrease, the signal to noise ratio (SNR) in the correlation
tables may become poor and some spurious vectors may appear in the PIV result. In order to retard
this problem, the Multiple Correlation Validation (MCV) technique was used in the present paper.
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Figure 3. The Multiple Correlation Validation technique for the Signal Noise Ratio improvement of
correlation tables
3. Multiple Correlation Validation (MCV) technique
Currently, most widely used methods to eliminate the spurious of the PIV results are conducted
in the velocity vector space as the post-processing step of the PIV image processing. By comparing
the vectors with their neighbours to determine if they are in some statistical or physical sense
inconsistent (Kimura et al.[5], Westerweel, [6]). These methods assumed that the resolution of PIV
result is high enough and the flow structures can be benign enough so that the apparent
discontinuities in the vector field will not present and be eliminated. The detected spurious vectors
always were replaced by the interpolated values. Such kind of method addresses only for the most
9th International Symposium on Flow Visualization, Heriot-Watt University, Edinburgh, 2000
Editors G M Carlomagno and I Grant.
137-4
IMPROVE THE SPATIAL RESOLUTION OF PIV RESULT BY USING HIERARCHICAL
RECURSIVE OPERATION
obviously correlation error and does not address the most subtle problems that severely limit the
sub-pixel accuracy and resolution. Although very useful, these post-interrogation validation
methods are not ideal.
Multiple-correlation validation technique is a new technique to do error correction, which was
firstly suggested by Hart [7,8]. It can do the error correction in the correlation table before the
velocity vectors are determined. It is based on the assumption of that the error or noise peak in the
correlation space resulting from insufficient data or correlation anomalies may be randomly. The
noise peaks will not appear at the same locations in the correlation tables for the different
interrogation windows. Hence, by the multiplication operation of the correlation table generated
during processing with the correlation table generated from one or more adjacent regions, the noise
peaks in the individual interrogation table can be eliminated in the correlation table after multiple
correlation validation operation. Thus, the correct peak in the correlation table due to displacements
of the tracer particles can be easily identified (Figure. 3). By using the different overlap
Interrogation window A
Interrogation window B
Overlap region of Interrogation window A and B
Hart’s arrangement (1998)
The spatial resolution in X and Y axial
direction is different
Interrogation window A
Interrogation window B
Overlap region of Interrogation window A and B
Present arrangement
The spatial resolution in X
and Y axial direction is same
a. Hart’s arrangement
b. present arrangement
Figure 4. The comparison of the interrogation window overlap arrangements for the Multiple
Correlation Validation (MCV) technique
arrangement of the multiplied interrogation windows, it was called Correlation Error Correction
method by Hart [7,8] and Checker Board Cross-correlation method by Okamoto [9].
According the research of Okamoto [9], the multiple-correlation validation operation can
improve the Signal Noise Ratio (SNR) in the correlation table about 3.5 times. Hart [8] also
reported that multiple correlation validation operation can improve sub-pixel accuracy, retard the
effect of the out-of-plane movement and velocity gradient effect by elimination anomalies in the
correlation table and strengthening the peak correlation signal. More detail can be got from the
papers of Hart [7,8] and Okamoto [9].
Unlike the overlap arrangement of the interrogation windows suggested by Hart [7,8] to shift the
interrogation window B half interrogation window size (Figure. 4(a.)). A new arrangement by
using an enlarged interrogation window B was suggested in the present paper (Figure 4(b)) with the
consideration of the spatial resolution. Since the velocity vector obtained after the multiplecorrelation validation operation is actually the average velocity of the particles in the overlap
region of the adjacent interrogation windows, the size of overlapped region determine the spatial
resolution level of the PIV result. So, the overlap arrangement suggested by the present paper over
Hart's arrangement is that it can insure the same spatial resolution level in the X and Y axial
direction for the PIV result.
Figure 5 shows the comparison of the PIV results from the same PIV images by using different
PIV image processing methods. It was well known that FFT based cross correlation method (FFTCC) method has the advantage of fast computational speed compared with conventional Direct
Cross Correlation (D-CC) method. However, since the FFT-CC method used a same interrogation
window size in the first and second PIV images, which may cause extra aliasing error and bias
error (Raffel et al. [10]) or the “out of pattern effect” (Huang et al., [11]) compared with
9th International Symposium on Flow Visualization, Heriot-Watt University, Edinburgh, 2000
Editors G M Carlomagno and I Grant.
137-5
Hui HU, Tetsuo SAGA, Toshio KOBAYASHI, Nobuyuki TANIGUCHI and Shigeki SEGAWA
conventional D-CC method. So, the image processing result by using FFT-CC method (Figure
5(a)) has more spurious vectors than that by using conventional D-CC method (Figure 5(b)).
Although conventional D-CC method used a bigger interrogation window at the second PIV
image to avoid the “out of pattern effect”, out-of-plane movement of the tracer particles or velocity
gradient effect may still result in the spurious vectors in the velocity vector fields (Figure 5(b)). By
using Multiple Correlation Validation (MCV) technique, the appearance of spurious vectors in the
PIV velocity field can be suppressed very much (Figure 5(c)). When the multiple correlation
validation operation was coupled with hierarchical recursive PIV operation, a more robust result for
spurious vector suppression and spatial resolution improvement can be obtained (Figure 5 (d)).
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Figure 5. The comparison of the PIV results from the different image processing method by using
same PIV images (interrogation window size 32 by 32 pixel)
4. Effect of the spatial resolution levels of PIV results on the small-scale vortex identification
capability in flow fields
In order to investigate the effect of the spatial resolution levels of PIV results on the smallscale vortex identification capability in the flow flied, the PIV results at different spatial resolution
levels will be compared qualitatively and quantitatively in the following context. These PIV results
were obtained from the same PIV images by using HR-PIV method with multiple correlation
validation operation for different final spatial resolution levels. The object flow fields are a circular
jet flow and a lobed jet mixing flow. All the PIV images used in the present paper were captured by
using a 1018 by 1008 cross correlation CCD camera (PIVCAM10-30), and all the velocity vectors
were in the 50% overlap grids of the interrogation window size for every spatial resolution level.
4.1. PIV results of a circular jet mixing flow
Figure 6 shows the PIV results in the axial slice of a circular jet flow at four different spatial
resolution levels from the same PIV images. The Reynolds number of the circular jet flow is about
9th International Symposium on Flow Visualization, Heriot-Watt University, Edinburgh, 2000
Editors G M Carlomagno and I Grant.
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IMPROVE THE SPATIAL RESOLUTION OF PIV RESULT BY USING HIERARCHICAL
RECURSIVE OPERATION
6,000 based on the jet velocity and diameter of the circular nozzle (D=30 mm). The interrogation
window sizes for these four spatial resolution levels are 64 by 64 pixel (Figure. 6(a)), 32 by 32
pixel (Figure. 6(b)), 16 by 16 pixel (Figure. 6(c)) and 8 by 8 pixel (Figure. 6(d)) respectively. The
PIV result at the first spatial resolution level corresponds to the PIV result from conventional
correlation PIV method by using big interrogation window size. Since the PIV velocity vector field
obtained by using correlation method is actually a spatial filtered velocity vector field, which is the
spatially averaged “transitional” motion of the particles in the interrogation window. Any
information on the velocity fluctuations and the rotational component of the velocity field within
the region of the flows covered by the interrogation windows is filtered out. So, the velocity vectors
field by using conventional correlation PIV method with big interrogation windows (64 by 64
pixel. Fig. 6a) is very smooth and only big vortices (spanwise roller structures due to the KelvinHelmholtz instability of the shear layer) can be seen in the flow field. When the spatial resolution
level improved to the second level, some smaller vortices and turbulence structures which were
filtered out in the first spatial resolution level (Fig. 6a) can be found now in the PIV velocity field
(Fig. 6b). As the spatial resolution improved further to third level (Fig. 6c) and fourth level (Fig.
6d), more and more velocity vectors can be obtained and more and more small scale vortical and
turbulent structures can be revealed in the PIV results.
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Figure 6. The PIV results of a circular jet flow (Re=6,000) with different spatial resolution
levels from the same PIV images
9th International Symposium on Flow Visualization, Heriot-Watt University, Edinburgh, 2000
Editors G M Carlomagno and I Grant.
137-7
Hui HU, Tetsuo SAGA, Toshio KOBAYASHI, Nobuyuki TANIGUCHI and Shigeki SEGAWA
In order to demonstrate the effect of the spatial resolution level of PIV result on the vortical
structures identification capability in the flow field more clearly, the zoom in figures of the big
vortices roller due to the Kelvin-Helmholtz instability were shown on the Figure. 7. It can be found
that the bigger roller show on Figure 7(a) is actually composed by many smaller scale vortices.
More and more small vortices can identified in the flow field and more and more local turbulence
movement features can be seen clearly in the velocity field as the spatial resolution level of the PIV
result increasing.
A quantitative comparison of the above PIV results at different spatial resolution levels was
shown on Figure 8(a), which are the velocity profiles at the near field of the circular jet. The zoomin velocity profiles of the shear layer between core jet and ambient flows were shown on Figure
8(b). Since most turbulence components less than the interrogation windows sizes are filtered out,
the velocity profile of the PIV result at the first spatial resolution level by using bigger
interrogation window (64 by 64 pixel) is found to be very smooth. As the PIV result spatial
resolution improving, the velocity profile was found to be more and more zigzag, these are due to
the fact that the more and more small-scale vortices and turbulence movements can be identified in
the PIV velocity vector field by using more and more smaller interrogation windows.
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Figure 7. Zoom-in of the big roller shown on Figuere 5
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Editors G M Carlomagno and I Grant.
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IMPROVE THE SPATIAL RESOLUTION OF PIV RESULT BY USING HIERARCHICAL
RECURSIVE OPERATION
9.0
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the second spatialresolution level(interrogation window size 32 by 32 pixel)
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Figure 8. The quantitative comparison of the PIV results at four spatial resolution levels
4.2. PIV results of a lobed jet mixing flow
A lobed nozzle, which consists of a splitter plate with a convoluted trailing edge, is an
extraordinary fluid mechanic device for efficient mixing of two co-flow streams with different
velocity, temperature and/or spices. The interaction of various vortical structures in lobed jet
mixing flows had been suggested to be the main reason for the jet-mixing enhancement (Hu et al.
[12]). Figure 9 shows the typical flow visualization results in the cross plane of a lobed jet mixing
flow by using Laser Induced Fluorescence (LIF) technique. The Reynolds number of the lobed jet
flow is about 3,000 based on the jet flow velocity and the diameter of the lobed nozzle (D=40mm).
It can be seen clearly that the large scale streamwise vortices generated by the six lobe structures
were found to be in the form of six “mushrooms” at the downstream of the lobe trailing edges.
Another six counter-rotating horseshoe vortex pairs, which have smaller scale, can also be found at
the downstream of the six lobe troughs.
9th International Symposium on Flow Visualization, Heriot-Watt University, Edinburgh, 2000
Editors G M Carlomagno and I Grant.
137-9
Hui HU, Tetsuo SAGA, Toshio KOBAYASHI, Nobuyuki TANIGUCHI and Shigeki SEGAWA
a. at time T=T0
b. at time T=T0+0.1s
Figure 9 LIF visulization results in the cross section of a lobed jet mixing flow
a. the first level (interrogation window 64 by 64 pixel)
b. second level (interrogation window 32 by 32 pixel)
c. the third level (interrogation window 16 by 16 pixel) b. the fourth level (interrogation window 8 by 8 pixel)
Figure 10. The PIV results at different spatial resolution levels from the same PIV images of a
lobed jet mixing flow
9th International Symposium on Flow Visualization, Heriot-Watt University, Edinburgh, 2000
Editors G M Carlomagno and I Grant.
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IMPROVE THE SPATIAL RESOLUTION OF PIV RESULT BY USING HIERARCHICAL
RECURSIVE OPERATION
Figure 10 shows the PIV results with four spatial resolution levels at the same Reynolds number
level and same downstream location (X/D=30mm) as above LIF visualisation results. From the
comparison of the PIV results at four spatial resolution levels, the effect of the PIV result spatial
resolution level on the small-scale vortex identification capability can be demonstrated more
clearly. At the first spatial resolution level (Fig.10a), the interrogation window size is 64 by 64
pixel, and just the obscure contour of the large streamwise vortical structures generated by six lobe
structures can be seen in the PIV velocity vector field. As the spatial resolution improved to the
second level, the interrogation window size decreases to 32 by 32 pixel (Fig. 10b), the large
streamwsie vortical structures which can not be revealed successfully in the first level can be
identified clearly in the PIV velocity vector field. The smaller horseshoe vortical structures at the
downstream of the lobe troughs can just obscurely identified. When the spatial resolution level
increased further to the third level, the interrogation window size decreased to 16 by 16 pixel (Fig.
10c), the smaller horseshoe vortical structure can be identified very clearly in the flow field as the
above LIF visualisation results. As the interrogation size decreased to the 8 by 8 pixel (level forth,
Fig. 10d), much more small-scale turbulence structures can be revealed in the PIV velocity vector
field.
Figure 11 shows the comparison of velocity spatial power spectrum of the above PIV results at
different spatial resolution levels. It can be seen that all the PIV results agrees with each other well
for the large scale components in the spectrum profiles, which means that all the PIV results can
reveal the large scale vortex structures in the flow field well. However, for the small-scale
components, the velocity spatial power spectrum profile of the PIV results with coarse spatial
resolution was found to be more smooth and smaller than that with finer spatial resolution. This is
because that all the fluctuation components which scale less than the size of the interrogation
window was filtered out, and can not be detected successfully in the PIV velocity vector field.
Power spectr
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40
interrogation window size (32 by 32 pixel)
35
interrogation window size (16 by 16 pixel)
30
interrogation window size (8 by 8 pixel)
25
20
15
10
5
0
10
100
1000
spatialscale (pixel)
Figure 11. Velocity spatial power spectrum of PIV results at different spatial resolution levels
5. Conclusion
A Hierarchical Recursive PIV (HR-PIV) image processing method which can improve the spatial
resolution of PIV results was described in the present paper. By staring with a large interrogation
window and search distance as the same as conventional correlation analysis based PIV image
processing methods, the resolution of the PIV result was improved through the hierarchical
reduction of the size of interrogation windows and search distance in the next iteration by using the
calculation results of former step. In order to improve the Signal Noise Ratio (SNR) in correlation
tables as the interrogation window size hierarchically decreasing, Multiple Correlation Validation
9th International Symposium on Flow Visualization, Heriot-Watt University, Edinburgh, 2000
Editors G M Carlomagno and I Grant.
137-11
Hui HU, Tetsuo SAGA, Toshio KOBAYASHI, Nobuyuki TANIGUCHI and Shigeki SEGAWA
technique was used to suppress the appearance of the spurious vectors. A new overlap arrangement
of the interrogation windows for the Multiple Correlation Validation technique was suggested in
the present paper, which can insure the same spatial resolution level in X and Y axial direction for
the PIV results. Hierarchical Recursive PIV (HR-PIV) algorithm with Multiple Correlation
Validation technique were used to PIV image processing of a circular jet flow and a lobed jet
mixing flow. By comparison of the PIV results at different spatial resolution levels quantitatively
and quantitatively, the effect of the spatial resolution of PIV results on the vortex and turbulence
structure identification capability in the flow field was also discussed in the present paper.
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9th International Symposium on Flow Visualization, Heriot-Watt University, Edinburgh, 2000
Editors G M Carlomagno and I Grant.
137-12