Dynamic PIV : a Strong Tool to Resolve the
Unsteady Phenomena.
K. Okamoto
The University of Tokyo, Tokai-mura, Ibaraki, 319-1188, JAPAN
okamoto@tokai.t.u-tokyo.ac.jp
Abstract
This paper describes the application and future of the Dynamic PIV method. It
consists of a high-speed camera with high-resolution, a high-speed pulse laser and
a synchronization system. The equipments are almost the same as for a conventional PIV system. However, it needs advanced software for the analysis of the
dynamic system. The current status of the Dynamic PIV is discussed. The future is
also shown through the application of Dynamic PIV.
1 Introduction
The two-dimensional PIV (2D2C) and stereo PIV (2D3C) system had already
been commercialized. In these standard PIV, high-resolution CCD camera and
Double pulse Nd:YAG laser are used. The image resolution is at least 1000 x 1000
pixel. Sometimes, 2000x2000 pixel CCD can be used. Because of the limits of the
camera's read-out time and laser reputation frequency, these PIV systems can
measure the flow field at about 4 to 15 Hz.
To improve the spatial resolution, many high-resolution PIV algorithms have
been proposed, including recursive PIV, gradient PIV and so on. The interrogation
area is now currently 16x16 and sometimes down to 4x4 pixel, resulting in
100,000 vectors in one image. Although the spatial resolution has been improved
significantly, the temporal resolution remains about 15 Hz. Therefore, using current PIV system, only a statistical analysis can usually be carried out.
Very little transient information is used. If the characteristics frequency of the
target flow field is much lower than 15 Hz, e.g., 1Hz, the measured data can be directly applied for transient analysis. However, it is a very limited field. The other
choice is the phase average analysis. When the phenomenon has certain periodicity, phase averaged vector fields can be measured with varying the measurement
timing.
Recently, because of the rapid progress of the high-speed digital camera, much
higher framing rates can be reached. Also, using a high-frequency pulsed laser as
18
an illumination, enough light (10 mJ) can be supplied to the target flow field of tipically 10 cm square.
In this paper, the current status of the Dynamic PIV system will be reviewed.
Then, the advantage of the Dynamic PIV will be discussed. Advanced PIV algorithms for Dynamic PIV will be proposed. The post processing technique for the
Dynamic PIV will be discussed.
2 Dynamic PIV System
(a) Camera
"Dynamic PIV" means high temporal resolution, that is a PIV system for analyzing the dynamical information in the flow field. Etoh et al., (2002) developed a
1,000,000 fps high-speed CCD camera with a 312x260 image resolutions, which
allows to resolves at most a 500KHz dynamics.
On the side of CMOS camera, several high speed camera had been commercialized. For example, the Photron FASTCAM Max120 (APX) can capture
1024x1024 pixel images at 2000fps. The image resolution is thus equivalent to the
current conventional PIV cameras, with a temporal resolution 70 times faster.
Also, the camera can capture 2048 images sequentially, corresponding to about 1 s
of the phenomenon. The quantization is done on 10 bits (1024) per pixel. The sensitivity is thus better than a conventional 8 bits CCD cameras.
Up to now, high-speed cameras used to sacrify the image resolution and number of images recorded in order to achieve the high frame rate. Now, CMOS cameras have enough resolution and store enough images for a useful PIV analysis.
This is their main advantage. Morover, these CMOS cameras can reduce the
framing rate to that of conventional PIV cameras. Therefore, they can be used also
for conventional PIV applications. The author believes that the CMOS cameras
will rapidly become the standard cameras for PIV.
(b) Pulse laser
In addition to the high-speed camera, the illumination tool is a key device. In a
conventional PIV system, the double pulse Nd:YAG laser is widely used. The
pulse energy is from 20 to 400 mJ. The interval between the pulses can be controllable to a nano second. However, the repetition rate is limited to be about 30
Hz.
The high power pulsed lasers developed for welding can be used for the highspeed illumination. The Coherent Corona is a Nd:YAG laser (λ = 532 nm), with a
repetition rate up to 25 kHz. The Peak power is 75 W, i.e. 7.5 mJ/pulse at 10 kHz.
The peak pulse energy is 14 mJ/pulse at 2 kHz.
Combining the 2 kHz CMOS camera with the Corona pulse laser, good quality
particle images can be captured every 0.5 ms (2kHz). For some water experiments, e.g., laboratory scale water jet, 0.5 ms time interval is short enough to extract the velocity distributions. When the characteristics frequency of the jet (e.g.,
Invited Lectures 19
St = 0.2) is less than 1kHz, the unsteady flow information can be obtained with a
2 kHz sampling rate. Then high spatial-resolution and high temporal-resolution
velocity vector can be measured using these cameras and lasers. In section 4, an
example of such an experiment will be described and discussed.
(c) Frame straddling
For experiments in air, an 0.5 ms time interval is usually not short enough.
Then, the frame straddling technique is also needed. To achieve the frame straddling illumination, twin cavity or double pulse single cavitylasers are needed.
In the twin system, two pulsed laser beams will be combined into one beam
(similar to the conventional PIV system). The advantages of the twin system are
(1) the controllability of the time interval between the two pulses and (2) similarity of the laser intensity. With synchronizing the twin lasers and camera, any time
interval can be generated. The time interval is limited by the high-speed camera
dead time. Since it is about 4 µs for this camera, the minimum time interval will
be 4 µs. The disadvantage of the twin system is the difficulty of the beam alignment.
On the other hand, double pulse single cavity lasers had been commercialized
in 2002. In this study, the Positive Light, Evolution-30 with double pulse option is
used. The laser rod is made of Nd:YLF (λ = 527nm). In this system, single pulse
is divided into double pulses, with controlling the Q-switch. The interval between
the double pulses can be varied from 1 to 100 µs. The repetition rate is 1 to
10kHz. The pulse energy is 10mJ/pulse at 1kHz in the double pulse mode. Since
the beam is generated by one rod, no beam alignment is needed. However, the
beam characteristics (e.g., pulse duration) of 1st pulse is slightly different from
that of the 2nd pulse. So, the user should take care the beam differences for the
frame straddling illumination. Synchronizing the double pulse system (1kHz /
double pulse mode) with the high-speed camera (2kHz), the velocity field can be
sampled at 1kHz. The time interval between the double pulses is also limited by
the camera dead time (4 µs).
3 Advanced PIV algorithms for Dynamic PIV
(1) PIV Algorithms
For the conventional PIV system, many PIV algorithms had been proposed
using the double images. Recursive PIV considering the image distortion is the
popular technique for the PIV now (e.g., Hart, 2000). In these techniques, the spatial resolution is improved dramatically, down to 8x8 pixel and in favourable
situations to 4x4 pixel.
Let us consider the PIV algorithm to be a low-pass filtering of the images. The
image has 8x8 pixel information, which will be converted into one velocity vector.
The velocity is the averaged displacement of the 8x8 pixel interrogation area. This
20
means that the obtained velocity is considered to be the low-pass filtered information of 8x8 images. This procedure is the spatial low-pass filtering.
In the Dynamic PIV, high temporal resolution images are captured. Therefore,
the temporal information can be used to get the velocity vectors. For example,
three or four temporal images can be used to calculate one velocity vector. A temporal averaging can be taken into account in advanced Dynamic PIV algorithm.
This procedure is then a spatial-temporal low-pass filtering.
Many spatial-temporal low-pass filtering algorithms can be considered. In this
paper, three types will be shown.
(2) Higher-order gradient method
Nishio and Okamoto (2003) have proposed advanced algorithms based on the
gradient method (Sugii et al, 2001). In the usual gradient method, the following
constraint equation is solved in a small interrogation area,
∂f
∂f
∂f
(1)
+u +v
=0
∂t
∂x
∂y
where f is the image grey level. In a higher-order method, this equation becomes :
 ∂f
1 ∂f  ∂u
∂u
∂u 
∂f
∂f 
 + u
 + u + v ∆t +
+ v ∆t 2
2
∂
∂
∂
∂y 
∂
∂
∂
t
x
y
x
t
x



1 ∂f  ∂v
1  ∂2 f
∂2 f
∂2 f 
∂v
∂v 
 + u + v ∆t 2 +  2 + u 2 2 + v 2 2 ∆t 2
+
2 ∂y  ∂t
2  ∂t
∂x
∂y 
∂x
∂y 
 ∂2 f
∂2 f
∂2 f  2
∆t = 0
+  u
+ uv
+v
∂x∂y
∂y∂t 
 ∂x∂t
(2)
Using several sequential images, the velocity term, , and the higher order terms,
can be directly calculated.
(3) Hybrid PIV/PTV
Hong (2003) proposed an hybrid technique of PIV and PTV. In the four-time
step PTV (Nishino et al., 1989), the particle movement was tracked for four time
steps. In Hong's technique, initially, the cross-correlation functions are calculated
for every sequential image :
C t ( p, q ) = ∑ f t (i, j ) f t +1 (i + p, j + q )
(3)
where superscript t means the temporal index and f is the image grey level. In the
correlation function, Ct, several peak locations are searched. Then, the peak location of the correlation functions is tracked for several sequential functions. The
same algorithms for the particle tracking techniques can be applied. The particle
location is replaced to the correlation peak location. Usually, there are several
Invited Lectures 21
peak locations in one correlation function. The correct peak is tracked among
several peaks through the temporal sequential correlation functions. This procedure is the same with four-time step tracking (e.g., Nishino et al., 1989). The peak
locations are calculated with sub-pixel accuracy.
(4) Lagrangian PIV
Okamoto and Sugii (2003) have proposed a higher order cross-correlation. In
the above techniques, the cross-correlation function or gradient functions are calculated at the same interrogation area. These procedures are considered to be the
Eular expressions. Here, the correlation function for a sequence of three images is
defined as follows :
C t ( p, q ) = ∑ f t −1 (i − p, j − q ) f t (i, j ) + ∑ f t (i, j ) f t +1 (i + p, j + q )
(4)
This correlation function is a Lagrangian expression. Also, the location of the
measured vector is the center of interrogation area at time t. Figure 1 shows the
example of the improvement of accuracy using the present technique using the
Standard Image #301 (Okamoto et al., 2001). The interrogation area is 4x4. Although there are so many peaks in the normal correlation field, there will be only
one peak for the present correlation field. Even when the interrogation area is only
4x4 pixel, the Lagrangian cross-correlation gives a single peak in the correlation
field. Because the information of the correlation function increases, the accuracy
also improves. The peak location also moves a little because of the temporal
variation of the vector. In the present case, the two correlations are added as
shown in Eq (4). The multiplication of the correlation can also be applicable,
which may be similar to Hart's algorithm (2000).
There will be many algorithms based on the similar concept, i.e., the temporalspatial low-pass filtering. With increasing the temporal directional averaging, spatial resolutions can be improved to be 1 pixel. (This is the original gradient technique (optical flow) proposed in 1980s).
For the recursive procedure, not only the spatial direction, but also the temporal
direction can be taken into account to increase the resolution.
(a)
(b)
Fig. 1. Improvement of correlation peak detection using Lagrange PIV. (a) Single
pair correlation. (b) Double pair correlation (Eq.(4)).
22
Y/D
1
0
-1
0
1
2
3
4
5
X/D
6
7
(a)
Fig. 3. Average velocity distributions
Fig. 2. Schematic of water jet experiment
100
Y/D=0.35, X/D=3
Suu
Svv
10
Spectral Density
0.0170281
1
0.119245
Y/D
0.204425
0
0.221462
0.170353
0.247016
1
0.1
-1
0
1
2
3
4
X/D
5
6
7
(b)
0.01
1
10
100
1000
Frequency (Hz)
2
Fig. 4. Fluctuating term( u ' )
Fig. 5. Spectrum of fluctuation
4 Application of Dynamic PIV
4.1 Water jet
Using the Dynamic PIV system, a water jet experiment was examined. Figure 2
shows the experimental set-up. The round jet is injected into a large open bath
(1200x600mm and 300 mm in depth). The jet nozzle is settled horizontally at the
center of the bath. The nozzle inner diameter, D, is 14 mm. The average velocity
of the jet is 650 mm/s, giving a Reynolds number Re = 9100. The viewing area is
from 0 to 6.6D downstream of the nozzle.
The characteristics frequency of the jet is estimated to be 20Hz, based on the
Strouhal number St = fD/U = 0.2. Therefore, recording 1000 velocity maps per
second allows to fully resolve the phenomenon in time.. The diameter of tracer
particle is 30 µm. The image resolution is 1024x512 pixel at 1000 fps. A single
pulse laser (Corona) is used for the illumination, synchronized with the camera
Invited Lectures 23
allowing to capture one image every millisecond. The number of images captured
in one set is 2048, corresponding to. about 2 seconds of the phenomenon. Considering the characteristics frequency, 20Hz, this total sampling timeis long enough
to capture the statistical flow field. By analyzing the sequential images, velocity
maps are obtained every 1ms. The experiment had been repeated 4 times, resulting
in 8 seconds of data.
The averaged velocity vector field is shown in Fig. 3. Figure 4 shows the dis2
tributions, u ' . The spectrum of the fluctuation in the shear layer (x/D = 3,
y/D=0.35) is shown in Fig. 5. The dominant frequency is confirmed to be about
15Hz. The 1000Hz sampling frequency and 2s sampling time are sufficient to
analyze the data. The temporal variation of the velocity will be analyzed in Section 5.
4.2 Mist jet into air (Hayami et al., 2003)
The above water jet experiment shows relatively slow transient. To investigate
the capability of extracting the fast transient, an air jet with mist is visualized. A
moisturizer is used for the mist jet generation. A double nozzle system with 120
degree angle generates tan air jet with small droplet. The upstream tank pressure is
set to be 0.2MPa, in gauge pressure. The light sheet is set horizontal and an area of
100mm downstream of nozzle is visualized using a double pulse laser system
(Evolution-30).
(a)
(b)
Fig. 6. Mist velocity distributions with 1kHz sampling (1024x1024 pixel). (a) Example of captured image. (b) Measured Velocity field.
In case 1, the camera framing rate is 2,000 fps, with 1024x1024 pixels. The
time interval between the double pulses is 0.1 ms , using theframe straddling technique. An example of captured image and measured velocity field are shown in
Fig. 6. High-resolution vector maps are captured at 1 kHz.
In case 2, the camera framing rate is 10,000 fps, with a 512x256 pixels resolution. In this case, the single pulse mode is used for the laser illumination, so that
the time interval between the images is 0.1ms. An example of captured image is
24
shown in Fig. 7. The mean velocity map for a total of 16,000 images is shown in
Fig. 8. Figure 9(a) shows the temporal variation of the velocity. The vortex motions can be observed in these figures. To emphasize the flow characteristics, the
fluctuating part of the velocity , i.e. u ' = u − U ., is shown in Fig 9b. In the fluctuation vector map, the vortex is clearly evidenced. Following the sequential vector map, the vortex transport is also easily recognized.
Fig. 7. Mist image with 10 kHz (512x256)
(a)
Fig. 8 Averaged Velocity vectors
(b)
Fig. 9. Temporal fluctuation of the mist flow (10kHz, 512x256). Instantaneous
velocity. (b) Fluctuation term (u').
Invited Lectures 25
5 Post-processing of the Dynamic PIV vectors
In the 2D PIV analysis, POD(Proper Orthogonal Decomposition) technique is
widely used. However, in these techniques, the temporal domain information is
not taken into account. Since there is enough information in the temporal direction
for Dynamic PIV, the three-dimensional (2D in space, 1D in time) POD analysis
can be carried out, showing the 3D dominant modes of the phenomenon. The details of the 3D-POD analysis for Dynamic PIV are discussed by Bi et al. (2003).
The 3D-POD analysis may also be considered as a low-pass filtering in 3D.
Fig. 10 shows the comparison of the spectrum between the measured data and
reconstructed POD data, (sum of first 6 modes). The original data is measured in
the water jet experiment described in Section 4.1. It shows that most of the energy
is contained in the first 6 modes in the present case.
Fig. 10. 3D-POD reconstructed spectrum
1 m/s
1.1
1 m/s
1.1
1
1
0.9
0.9
0.8
0.8
0.7
0.6
Y/D
Y/D
0.7
0.5
0.4
0.5
0.3
0.2
0.2
0.1
0
0.6
0.4
0.3
0.1
2
3
4
X/D
5
(a)
0
2
3
4
X/D
5
(b)
(a)
(b)
Fig. 11. Comparison between the measured and reconstructed vector. (a) Measured vector. (b) Reconstructed vector (Sum of first 6 modes).
Fig. 11 shows the instantaneous velocity distribution and the reconstructed one.
The basic component of the flow structure is correctly reconstructed. The noise
and error are considered to belong to the higher order mode, they can be removed
by the POD analysis. It is considered to b e the low-pass filtering in 3D frequency
domain (2D spatial + 1D temporal). Since the dominant first 6 modes are 3D, it is
26
very difficult to show them in 2D on paper. They are displayed as a movie file at
the following URL (http://www.utnl.jp/~okamoto/3dpod/).
6 Conclusion
As was illustrated in the present contribution, Dynamic PIV can provide a new insight in the unsteady aspects of flow fields. By providing a large amount of good
quality data, it can resolve quantitatively the dynamics of the flow field. Dynamic
PIV will surely be soon a standard tool for transient flow analysis. Based on the
present experience, for further evaluation on the dynamics of the flow field, the
following procedure should be investigated.
1) To obtain highly-reliable velocity data, the low-pass filtering technique in
both the spatial and temporal domains should be standardized, including the
PIV evaluation algorithm.
2) To analyze the spatio-temporal information, the three-dimensional POD technique works well as a post processing tool, allowing to retaine the most energetic modes and to remove most of the PIV noise.
3) Advanced techniques for comparison between the measured results and computer simulations will be needed. Both spatial and temporal frequency analysis will also benecessary. The wavelet analysis and advanced POD analysis
should be applicable.
Acknowledgement
A part of this work is carried out under the support of JSPS Grant-in-aid for scientific research A (No.14205031, Prof. Hayami, Kyushu University). The author
would like to express special thanks to Prof. H. Hayami and Mr. S. Aramaki, Kyushu University, and Dr. Y. Sugii and Dr. W.T. Bi, The University of Tokyo.
References
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Invited Lectures 27
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