3-D flow around an obstacle in narrow channel via Digital holographic PTV
by
Shin-ichi Satake (1) , Tomoaki Kunugi (2) , Kazuho Sato (3) and Tomoyoshi Ito (4)
Department of Applied Electronics, Tokyo University of Science
2641 Yamazaki, Noda, Chiba, 278-8510, Japan
(1)
E-Mail: satake@te.noda.tus.ac.jp
Department of Nuclear Engineering, Graduate School of Engineering, Kyoto University,
Yoshida, Sakyo, Kyoto 606-8501, Japan
(2)
E-Mail:kunugi@nucleng.kyoto-u.ac.jp
Toyota Industries Corp.,
2-1 Toyoda cyou, Kariya, Aichi 448-8671, Japan
(3)
E-Mail: kazuho.sato@mail.toyota-shokki.co.jp
Department of Medical System Engineering, Chiba University
1-33 Yayoi, Inage-ku, Chiba 263-8522, Japan
(4)
E-Mail: itot@faculty.chiba-u.jp
ABSTRACT
Digital holographic particle tracking velocimetry (PTV) is developed by single high-speed camera and single double
pulsed laser with high frequency pulses. This system can directly capture 1000 hologram fringe images for 1 second
through a camera computer memory. The 3-D particle location is made of the reconstruction by using a computer
hologram algorithm in PC cluster. This system can successfully be applied to instantaneous 3-D velocity measurement in
the water flow with a square or a circular cylinder obstacle, and can obtain an average of 170 instantaneous velocity
vectors.
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1. INTRODUCTION
Holographic particle image velocimetry has been adopted using photographic film (Barnhart et al. (1994), Meng and
Hussain (1995), Sheng et al.(2003)).This system has high quality flow information and recording of an instantaneous 3-D
velocity field illuminated by one beam line. These characteristics are a big advantage over other Particle Image
Velocimetry method. However the technique takes up most of the reconstruction process time, and it is difficult to
capture the time evolution of a particle image by a single frame recording of instantaneous particles dispersed in a flow
field. On the other hand, digital holographic techniques easily capture the time evolution of particles by digital camera.
But they are only used for in-line holograms (Schnars and Juptner(1994), Murata and Yasuda (2000)) due to the limitation
of digital camera resolutions, and require high-speed computer performance to reconstruct particle location by a
computer hologram algorithm. Furthermore, the computational cost is increased if it is used for reconstruction of
particles by a high-speed camera owing to the increase in the fringe image frame. However, the particle field of the highspeed reconstruction has recently been successful using the Fast Fourier Transform technique with Fresnel diffraction
equation for the computer hologram calculation (Schnars and Juptner(1994), Murata and Yasuda (2000)). However, the
result by the FFT method (Murata and Yasuda (2000)) was only used for the evaluation of reconstruction of steady
particles. Therefore, we developed a complete digital holographic PTV system without photographic film, and the 3D
velocity vectors in our system can be taken by one high speed digital camera ( Satake et al. (2004)). Furthermore, the 3D
vectors obtained have time evolutions with the repetition time of 1 KHz; that is, high speed measurements in fluids can
be obtained. The present system is applied to measure instantaneous 3-D velocity vectors by tracking tracer particles in
a water flow field with a square or a circular cylinder.
2. EXPERIMENTAL METHOD and PROCEDURES
2.1 Optical setup
Figure 1 shows the optical setup. The optical system consists of a single high-speed camera, a single laser, one filter,
one beam expander, and attenuator. Nd:YLF laser (Photonic Industries DS20-527, λ =527 nm) is used as a light source,
which gives a pair of laser pulses at a repetition rate of 1kHz. The hologram fringe images are captured through a highresolution digital CCD camera (Visionresearch, Phanton V5.0) without a lens, which has a resolution of 1024 x 1024 (16
µm / pixel). The camera and the laser are synchronized by a pulse generator unit. This system with straight light line and
without mirror is different from previous our one ( Satake et al. (2004)). The outline of a test section is shown in Fig. 2.
The flow system is the channel flow enclosed with the two 2mm glass plates, and has a channel width of 4mm. The
working fluid travels through the two holes on the bottom plate. The obstacle is made of brass, 4 mm3 is size. The
working fluid is water, which is maintained at 33 degrees Celsius, and the supplied particle is a 50-micron nylon spherical
particle (ρ t/ρ f=1.05). The water is driven by pump, and a fixed speed is maintained by using the valve. The measurement
period is 1 second, and flow velocity is 15.3 mm/sec. The Reynolds number based on the length of square and the bulk
velocity is approximately 89. The reconstruction of particles from the fringe images in x-y directions is done by FFT
technique with Fresnel diffraction equation (Schnars and Juptner(1994), Murata and Yasuda (2000)). The FFT technique
was used for the following transform procedures:
h( x , y , z ; g (ξ ,η )) =
∞ ∞
1
∫ ∫ g (ξ ,η ) jλ z e
j (2π / λ ){( z + (( ξ− x) 2+ (η−y ) 2) / 2z }
dξ dη
−∞−∞
∞ ∞
=∫
∫ g (ξ ,η ) g
F
(x − ξ , y − η )dξ dη
(1)
−∞−∞
•@
=ℑ [ℑ( g )ℑ(g F )].
-1
2
The calculation of 3D particle reconstruction was carried out from a reproduction in 200 divided sections in z-direction
for a channel width of 4mm. Calculation of the particle locations in this direction is done by looking for the local minimum
points in the gradation image of the reconstructed particles. For example, in fig. 3 (a), the profiles of particle brightness is
right for the center on particle’s fringe. On the other hand, the brightness in fig 3(b) is not good for hyperboloid of
revolution of one sheet except for the centre of the particle’s fringe. Our search program can distinguish both cases and
can only detect right particle brightness. The 3-D tracking of the reconstructed particle positions is used for two frames
in the time evolution. Since the pulse interval was short, time interval of the particle tracking is sufficient. These
procedures for the reconstruction and particle tracking with 1000 fringe images required calculations of 200 x 1000 times
for FFT, few hours using PC cluster constructed for five personal computers. In this research, 1500 particles per frame
were reconstructed, and an average of 170 instantaneous velocity vectors was obtained.
Laser
Attenuator
Beam
Filter
Flow Channel
Camera
y
Expander
z
Rail
Fig. 1. Optical
setup
2 mm 4 mm 2 mm
7.5 mm
4.0 mm
φ 4.8 mm
4.0 mm
35.0 mm
63.0 mm
18.5 mm
18.5 mm
Y
7.5 mm
X
X
Glass plate
Spacer
Glass plate
Z
9.5 mm
Out flow
In flow
Fig. 2. Test section in flow channel
3
9.5 mm
Particle’s fringe
Particle
Z
X
Y
Fig. 3.
Particle search to the z-direction: (a) Right particle, (b) unsearched particle
3. RESULTS AND DISCUSSION
The mean velocity profile without an obstacle is shown in Fig. 4. The laminar flow was obtained by our system to check
the accuracy of measurement. The velocity profile was in good agreement with laminar theory. The error of the velocity
is less than 5%. The picture of the fringe image is shown in Fig. 5. The square black shadow in the image is an obstacle,
which is 4mm for one-side of square. The fringe image is moving downward from the top to the bottom. Many fringes
appear and are clearly captured in each frame. Moreover, it is considered that the stationary fringe is sticking to the glass
side. The picture of the reconstructed image is shown in Fig. 6, where the reconstructions of particles by the computer
hologram algorithm are 30.42 mm from the CCD surface for a square obstacle. The reproduced particles were observed
from between 28.42 and 32.42 mm from this surface. It is clear that the reproduced particles are moving right hand side
from the left hand side. Moreover, an inverse flow is clearly captured around the obstacle. The stationary fringe images
in Fig. 5, on the other hand, are the stationary particles, and are removed from each image as a grand picture when the
particles are tracked. Figure 6 (a) (b) show their reconstruction. The particles number 1558 for square obstacle and 2021
for circular cylinder; most of them are uniformly distributed. The instantaneous velocity vectors obtained are only
shown in Fig. 8 (a) (b), although we photographed the time evolution of these vectors for 1 second (not shown). It can
be seen that the flow is from the upstream to the lower stream around the obstacle, and that the inverse flow occurs
around the obstacle, which is the stagnation point. The instantaneous velocity vectors on the images do not drastically
change because the flow speed is relatively slow. The average of 170 instantaneous velocity vectors was obtained from
the 1558 particles reconstructed.
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Fig.4.
(a)
Mean velocity profile without an obstacle for laminar flow
(b)
x
x
y
y
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Fig. 5. Fringe images of particles around an obstacle: (a) a square, (b) a circular
cylinder
x
x
y
y
Fig. 6. Reconstruction of particles in x-y plane: (a) a square at 30.42 mm, (b) a circular cylinder
at 29.72 mm
Fig. 7. Reconstruction of particle: (a) a square, (b) a circular cylinder
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Fig. 8. Three-dimensional velocity vectors around an obstacle: (a) a square, (b) a circular
cylinder
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4. SUMMARY
In conclusion, a digital holographic particle tracking velocimetry system is successfully applied to a 3-D transient flow
around an obstacle in a narrow channel with a single high-speed camera and a high frequency double pulsed laser. The
average of 170 instantaneous velocity vectors is obtained by reconstruction and tracking with the time of evolution of
recorded fringes images. In the near future, we will apply this technique to a turbulent flow using a faster algorithm of
particle reconstruction with a special-purpose computer system composed of large-scale FPGA (Field Programmable Gate
Array) chips.
ACKNOWLEDGMENTS
The authors appreciated Mr Kazunori. Maruya at Rayture system Co., Ltd for laser set-up, and Mr Masayuki
Itakura at Seika Corporation for high speed camera, Keizo Okamoto at KGT for visualization supports. The authors would
express their appreciation to Mr. Keisuke Yamamoto and Hiroyuki Kanamori (Graduate students at Tokyo University of
Science) for their help in preparing computation and visualization.
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