The Local Field Correction Advanced PIV
Algorithm
J. Nogueira, A. Lecuona, A. Acosta and P. A. Rodríguez.
Department of Thermal Engineering and Fluids, University Carlos III de Madrid.
c/ Butarque 15, 28911-Leganés, Madrid, Spain. Goriba@ing.uc3m.es
Abstract
Local field correction particle image velocimetry (LFCPIV), is a correlation PIV
method able to accurately resolve flow structures smaller than the interrogation
window. It presents advantages over conventional PIV, offering an alternative in
the field of advanced and super-resolution PIV methods. Within the European
project Europiv2, the method has been refined and extensively tested. In the present work, the basics of the method are reviewed. This allows defining the range
where it offers an improvement over other methods. Issues concerning resolution,
peak-locking, group-locking and other metrological parameters are also commented, as well as differences with other advanced PIV techniques. Results on
real PIV images obtained by partners within Europiv2 are presented. These results
give an idea of the performance enhancement of LFCPIV in respect to conventional PIV. Furthermore, the ability to cope with high gradients in velocity, background features and the presence of solid boundaries is highlighted.
1 Introduction and Review of the Basic Principles.
Local field correction particle image velocimetry (LFCPIV) was first presented by
Nogueira (1997). It is a correlation PIV method able to accurately resolve flow
structures smaller than the interrogation window. This is achieved by the interaction of two additional features in respect to a conventional PIV method. These
features are: (i) the use of deformation, or distortion, to compensate the particle
pattern deformation caused by the non homogeneous displacement field, first proposed by Huang et al. 1993, and (ii) the use of a window weighting to avoid instabilities from spatial wavelengths smaller than the interrogation window (Nogueira
1997). Joining these two concepts is the only way found to succeed in obtaining a
non divergent distortion process and a non low-pass PIV result. These basic principles have been also published in Nogueira et al. (1999), but the up to date way
of implementing the method has been refined and simplified within the Europiv2
consortium (Nogueira et al. 2001a and Lecuona et al. 2002a).
In the field of advanced methods in two-dimensional PIV, when focusing on
high spatial resolution, there are two other branches in the research effort, apart
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from LFCPIV. One concerns hybrid methods. In these methods the initial steps are
implemented by classical correlation PIV. This gives a first measure of the local
velocity, allowing to resolve the smaller spatial scales by PTV (Particle Tracking
Velocimetry) with a higher accuracy (Keane et al. 1995 and Cowen and Monismith 1997, among others). The other branch is related to multigrid PIV, where the
size of the interrogation window is progressively reduced to increase spatial resolution (Soria 1996, Hart 1999, Scarano and Riethmuller 2000 and Lecordier et al.
2001, Rohaly et al. 2002, among others).
The main difference between LFCPIV and the hybrid techniques is that the
former does not have to identify and separate individual particles or clusters. This
allows the use of the method in PIV images with high seeding densities, besides
non-perfect focusing (e. g. stereoscopy), particle polydispersivity and high background noise.
Alternatively, when compared to the multigrid schemes, LFCPIV does not have
to reduce the size of the interrogation window. This allows for robustness, giving
good measurements in presence of different sources of noise.
The use of image distortion techniques allows for the measurement of large
velocity gradients, besides other advantages. Combined with a proper weighting,
the image distortion technique removes the interrogation window size as a limiting
factor.
These characteristics make LFCPIV of interest when dealing with measurements in large industrial wind tunnels.
The common drawback of iterative PIV techniques is the need of a computing
time longer than other algorithms. This time has been characterized for LFCPIV in
Lecuona et al. (2002a). Nevertheless, the time reported there was based on the
time required for a 64 by 64 FFT, which is somehow large in the current software
implementation when compared with current practice. This indicates that more refined programming of the actual algorithms could further reduce the required time.
Computer power growth may also reduce this drawback in the future. On the other
hand, the price to pay for the industrial wind tunnel time is high enough to justify
extra off-line PC time to extract the most information from the images.
2 Range of Applicability
The use of advanced algorithms is always more complex and/or time consuming
than conventional PIV. Consequently, it is interesting to know what the range of
applicability is in comparison with the conventional method. This way, a better
decision can be taken about its suitability for a certain task. Here the range of applicability of LFCPIV is briefly summarized.
The maximum allowable velocity gradient in a conventional PIV measurement
is in the range of ~ 0.03 ∆t-1 (Keane and Adrian 1993) for a particle image diameter in the order of 2 pixels. Even considering that this gradient is simultaneously
present in both perpendicular directions, the maximum value for the out-of-plane
component of the vorticity (curl of velocity) that can be measured with this limit is
in the range of ~ 0.06 ∆t-1. LFCPIV yields good vorticity measurements (error
Advanced Algoritms 87
smaller than 10%) up to ~ 1 ∆t-1 with synthetic images without any noise, and up
to ~ 0.6 ∆t-1 (Nogueira et al. 2001a and Lecuona et a1. 2002) with reasonable and
realistic sources of error. This can be also observed in the work “Assessment of
vorticity with advanced PIV techniques” within this book.
Another important issue in the description of the features of a flow is the smallest spatial wavelength λ that can be correctly described. In any case, the seeding
density should be high enough for the description of these wavelengths i.e. mean
distance between particles < ∼ λ/2. An additional limit when using conventional
PIV to describe small wavelengths, with errors in the order of 10%, is λ > ∼4F
(Willert and Gharib, 1991); where F is the side length of the interrogation window.
In the case of using LFCPIV, and with dense enough seeding, wavelength
structures of approximately 22 pixels have been successfully described with errors
smaller than 10%. In presence of other reasonable sources of noise, this limit may
be around 30 pixels (Nogueira et al. 1999).
Obviously, the description of any λ is also linked in every method to grid distances ∆ < ~ λ/2.
Only the image sensor limitations (Westerweel 1998) produce peak-locking in
the LFCPIV method. It is not impaired by other peak-locking sources that affect
conventional PIV (Nogueira et al. 2001b).
The LFCPIV method is also free of some of the non-linear bias of conventional
PIV like group-locking (Lecuona et al. 2002b).
Some more insight in these topics is offered in the following section by analysis
of the performance on real images.
3 Performance on Real Images
Performance results with synthetic PIV images have been published already.
These studies have been performed including noise (Nogueira et al. 1999 and
2001a) and also in noise-free synthetic images (Lecuona et al. 2002a).
This has allowed quantifying some of the errors to be expected. In this work the
focus is fixed on real images from within the Europiv2 consortium. Even though
in real images the errors can not be directly quantified, some aspects of the results
illustrate on the behaviour of the method.
This information also complements the available comparisons from the international collaboration Pivchallenge 2001 (www.pivchallenge.org). There, the performance of LFCPIV on synthetic images with known flow fields was compared
with other leading advanced algorithms.
Here the comparison is done with a conventional PIV method, as the advanced
algorithm application on real images from industrial wind tunnels is still an open
question under research.
For the implementation of conventional PIV, commercial correlation software
from a main supplier outside Europiv 2 has been chosen. It includes integer window offset but no image distortion. The scheme to infer the window offset to be
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used for the end single pass processing is a three steps multigrid. The window
sizes F are 128, 64 and 32 pixels in the three successive steps. In such a system
the only specifications left are the subpixel peak-fitting and the validation algorithms. These were found to be not relevant in our case as a second commercial
supplier and in-house conventional algorithms gave very similar results.
3.1 Peak-locking
As commented before, peak-locking may come from physical limitations of the
image sensor in relation to the window size (Westerweel 1998) or from other
sources (Nogueira et al. 2001b). The former source is unavoidable for small particle image diameters. The other sources are dependent on the PIV processing
method. For the evaluation of this peak-locking effect, an image from the DLRAirbus Bremen campaign in Europiv2 was selected.
This test campaign focuses on the 2D low Mach number aerodynamics around
an aircraft wing profile in high lift configuration. Fig. 1 gives a sketch of the position chosen for the image analyzed in this subsection.
Fig. 1. Location of the PIV image to be analyzed in this subsection.
The main objective here is to test peak-locking and not the robustness of
LFCPIV. Consequently, for this demonstration an easy case from the test campaign was selected. A more difficult case in the same location can be found in the
work “Assessment of vorticity with advanced PIV techniques” within this book.
In order to have a sketch of the flow field features, fig. 2 shows the vorticity
colour contours obtained with LFCPIV and with the conventional method.
In the analysis, parts of the image were masked. This was implemented in two
ways. On the solids, zero velocity was assumed (lines pattern in the figures).
Where shadows or obscuration precluded obtaining data in a flow field zone a free
value of the velocity was allowed but discarded as valid measurements (dots pattern in the figures).
Visualizing peak-locking is commonly performed using histograms of the vx
and vy velocity components. Here, a different approach has been chosen in order to
show the spatial distribution of this parameter. In figs. 3 and 4, the locations with
velocities within ±0.25 pixels from an integer value are shown black painted. The
locations with velocities out of this range are white painted. No peak-locking will
show equal black and white areas.
There is a clear difference showing less peak-locking in the LFCPIV processing.
Advanced Algoritms 89
a
b
Fig. 2. Vorticity plots showing the features within the flow. a) LFCPIV processing. b) conventional PIV processing.
a
b
Fig. 3. vx plots. Black: datum within ±0.25 pixels of an integer value. White: out of this
range. a) LFCPIV processing, 63% black, 37% white. b) conventional PIV processing, 80%
black, 20% white.
Smaller peak-locking does not necessarily means a better measurement. Actually, a reduction of peak-locking can be obtained even by means of a simple lowpass filter. This is one of the reasons for showing these plots instead of the usual
histograms. The information given by these plots show for LFCPIV the presence
of strong spatial variations located in the vortex street appearing in the wake of the
slat. This indicates the lack of low-pass effect. Even though, results with real images can not be fully conclusive, this is obviously only indicative.
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a
b
Fig. 4. vy plots. Black within ± 0.25 pixels of an integer. White: out of this range. a)
LFCPIV processing, 54% black, 46% white. b) conventional PIV processing, 72% black,
28% white.
3.2 Local correlation coefficients
The compensation of the particle pattern deformation by means of image distortion can considerably enhance the signal to noise ratio in presence of displacement
gradients. This was shown in a real case in Nogueira et al. (2001a). Here another
side of this enhancement is tested. One of the results of the signal to noise enhancement is the increase of the local correlation value when the correct image
distortion is performed, or at least an approximation. Consequently, given a certain PIV obtained velocity flowfield, its correctness can be tested by the analysis
of the local correlation coefficients that arise by distorting the original images according to it. Two cases from the DLR-Airbus Bremen campaign are depicted
here. Fig. 5 gives a sketch of the position chosen for the first case.
Fig. 6 shows the outputs from LFCPIV and conventional PIV in terms of vorticity. Inspecting these outputs the question of whether there is a recirculation
bubble with a reattachment in the upper-left part arises (like the conventional PIV
depicts) or the boundary layer is attached in that zone (like the LFCPIV depicts).
Inspecting the vector plot did not show more information as the width of the region is too small.
To check both possibilities, the respective flow fields have been used to distort
the original PIV images. Then the local correlation coefficients were calculated. In
this calculation the mean grey level of the original images was subtracted. Consequently, the value of the calculated coefficients varies between -1 and 1. Nevertheless, all the negative values have been set to 0 and labelled as non correlated.
The results are depicted in fig. 7.
Advanced Algoritms 91
Fig.5. Location of the PIV image analyzed in figures 6 and 7.
a
b
Fig. 6. Vorticity plots showing the features within the flow. a) LFCPIV realization b) conventional PIV realization.
a
b
Fig. 7. Local correlation plots. Grey scale: black <= 0; white = 1. a) LFCPIV processing. b)
conventional PIV processing.
The low value of the correlation coefficients inside the hypothetical bubble increases the credibility of the much more correlated results of LFCPIV. In fact, in
this run only 5 vectors out of a total of 12 959 had a negative local correlation
value. In the commercial PIV case, there were 94 of these vectors, 14 of them inside the supposed recirculation bubble.
There is a false high correlation thinner region; it is due to the strong reflections
near the profile surface, which correlates with itself.
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A second case corresponds to an image located at the trailing edge of the profile. It shows vorticity structures more difficult to analyse. The location of this
case is sketched in Fig. 8. The different outputs from LFCPIV and conventional
PIV are presented in Fig. 9. Here the main differences are in the lower right part of
the image.
Again using the local correlation coefficients a picture of a much more difficult
condition appears. This is depicted in Fig. 10.
Fig. 8. Location of the PIV image analyzed in figures 9 and 10.
a
b
Fig. 9. Vorticity plots showing the features within the flow. a) LFCPIV processing,
b) conventional PIV processing.
a
b
Fig. 10. Local correlation plots. Grey scale: black <= 0; white = 1. a) LFCPIV processing.
b) conventional PIV processing.
The lower left corner, where different outputs are located, is enhanced in the
LFCPIV case. The center lower part shows a high correlation zone in coherence
Advanced Algoritms 93
with a lower vorticity being there. The lower right part of the image shows a low
coherence zone that is produced by fainter illumination in the original images. Out
of 18,300 vectors output in both cases, only 332 do not give positive correlation in
the LFCPIV case. This number grows to 1,659 in the conventional PIV case.
3.3 Robustness
In the previous subsections, examples of performance in presence of large gradients were presented. Nevertheless, the robustness of the method does not only deal
with the ability to describe small scale features of the flow but also deals with the
behaviour in presence of noise and other common difficulties. In the previous
cases solid boundaries could be masked as they were outside of the area giving information of the flowfield. In some other cases this is not possible, and some
background incorporates on top of it the flow field information. This is the case
for the following example, whose PIV image was provided by DLR.
Fig. 11. Vorticity plot superimposed to the LFCPIV processed PIV image. The size of the
image is 1280 by 1024 pixels. Vorticity scale is on the right, the colour code allowes viewing the image.
Fig. 11 shows the vorticity contours superimposed to the original raw PIV image. In this case, the particle pattern to process was laid over a black background
in some parts of the image, as usual; and over the wing image in the rest. The grey
levels of the wing image even reached saturation of the CCD in some parts of its
lower trailing edge. In this situation, the large window size of the LFCPIV method
allows for the algorithms to successfully extract the velocity flowfield with high
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spatial resolution. This is due to the fact that spatial resolution is not limited by the
size of the interrogation window in this method.
On the other hand, the large window size prevents the method to give outliers
on the difficult areas.
Performance of LFCPIV in presence of large differences in local illumination
has been already tested in the Pivchallenge 2001 on synthetic images. With real
images like the one here studied, the results are more difficult to evaluate. Additionally, in this case the local correlation coefficients are usually large due to the
background light coming from the wing. This does not mean necessarily a good
measurement. Consequently, this parameter is not valid as a quality indicator.
To evaluate the output presented in this subsection, three independent and different processings were performed of the area with the wingtip vortex by means of
LFCPIV, using different grid nodes distances. This gives a picture at three different spatial resolutions, increasing the noise effects as the resolution increases and
supposedly revealing numerical artefacts of the method. The results are depicted
in Fig. 12.
16 pix. grid distance:
25 by 21 vectors.
0.19 % interpolated.
8 pix. grid distance:
51 by 43 vectors.
0.23 % interpolated.
(none in the vortex)
4 pix. grid distance:
101 by 85 vectors.
7.2 % interpolated.
Fig. 12. Vorticity from three different LFCPIV processings, varying the spatial resolution.
Same scale than figure 11.
It is apparent in the plots that the method is not creating false vorticity by numerical artifacts. No alternate vorticity structures, coming from vector outliers, are
evident. The three plots are consistently giving the same vorticity shape. The peak
growth is caused by the higher spatial resolution and the corresponding higher
contribution of background noise.
These results, although non conclusive, increase the confidence on the presence
of the internal vortex structure revealed by LFCPIV.
Advanced Algoritms 95
Conclusions
The LFCPIV advanced method, refined and metrologically characterised within
Europiv2 can be applied successfully to PIV images from industrial wind tunnel
facilities.
This method shows enhanced performance in respect to conventional PIV
methods in respect to: velocity gradients, spatial resolution, peak-locking and robustness.
The main drawback is the consumption of a larger computing time in respect to
conventional PIV (Lecuona et al. 2002a).
Acknowledgments
The authors would like to thank Dr. Kompenhans, Mr Alistair and the whole
group from DLR and Airbus for providing the PIV images.
This work has been performed under the EUROPIV 2 project: EUROPIV 2 (A
Joint Program to Improve PIV Performance for Industry and Research) is a collaboration between LML URA CNRS 1441, Dassault Aviation, DASA, ITAP,
CIRA, DLR, ISL, NLR, ONERA, DNW and the universities of Delft, Madrid,
Oldenburg, Rome, Rouen (CORIA URA CNRS 230), St Etienne (TSI URA
CNRS 842) and Zaragoza. The project is managed by LML URA CNRS 1441
and is funded by the CEC under the IMT initiative (contract no: GRD1-199910835).
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