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X-ray particle image velocimetry for measuring quantitative flow information inside
opaque objects
Sang-Joon Lee and Guk-Bae Kim
Citation: Journal of Applied Physics 94, 3620 (2003); doi: 10.1063/1.1599981
View online: http://dx.doi.org/10.1063/1.1599981
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JOURNAL OF APPLIED PHYSICS
VOLUME 94, NUMBER 5
1 SEPTEMBER 2003
X-ray particle image velocimetry for measuring quantitative flow
information inside opaque objects
Sang-Joon Leea) and Guk-Bae Kim
Department of Mechanical Engineering, Pohang University of Science and Technology, San 31,
Hyoja-dong, Pohang 790-784, South Korea
共Received 6 May 2003; accepted 18 June 2003兲
An x-ray particle image velocimetry 共PIV兲 technique was developed to measure quantitative
information on flows inside opaque objects. To acquire x-ray images suitable for PIV velocity field
measurements, refraction-based edge enhancement was employed using detectable tracer particles
with the object and detector separated by an experimentally determined optimal distance. The x-ray
PIV method was applied to a flow in an opaque Teflon tube. The resulting amassed velocity field
data were in reasonable agreement with theoretical predictions. © 2003 American Institute of
Physics. 关DOI: 10.1063/1.1599981兴
I. INTRODUCTION
Flow visualization has become an indispensable tool in
the investigation of complex flow structures. Recent advances in digital image processing techniques have made it
possible to extract quantitative information from visualized
flow images. In contrast to conventional pointwise velocity
measurement devices such as hot-wire anemometry or laser
Doppler velocimetry, the generation of quantitative flow visualization methods enable the rapid collection of data covering the entire velocity field. Particle image velocimetry
共PIV兲, which uses digital image processing of tracer particles
seeded in a flow, has come to be accepted as a reliable and
powerful velocity field measurement technique.1
The basic principle of PIV is as follows.1 Tracer particles
are seeded into the flow of interest and images of those particles are recorded twice with a short time interval (⌬t) on a
recording medium such as a charge coupled device 共CCD兲
camera. Particle displacements are then determined by comparing the two flow images; these displacements are divided
by the time interval ⌬t to extract the instantaneous velocity
field data. By ensemble averaging many instantaneous velocity fields, the spatial distributions of the mean velocity or
turbulent statistics of the flow can be obtained.
Because conventional PIV systems use a laser as the
light source, they can be applied only to transparent fluids
with a transparent window. Therefore, conventional PIV
technique is ill suited to measuring the flow characteristics of
nontransparent fluids or fluids confined in opaque materials.
To overcome these limitations of conventional PIV, we need
to use a transmission-type light source such as an x-ray or
ultrasonic wave source instead of a laser. In the present
study, we developed a PIV velocity field measurement technique in which an x-ray beam is the light source. For measuring flow velocity fields using this technique, we established an x-ray image enhancement method and optimized
the experimental conditions such as the object–detector disa兲
Author to whom correspondence should be addressed; electronic mail:
[email protected]
tance and type of tracer particle. The measurement of the
entire velocity field of a single-phase flow enclosed in an
opaque material has not been reported yet.
To visualize tracer particles inside an opaque tube, third
generation synchrotron radiation sources of the Pohang Light
Source 共Pohang, Korea兲 were used. The high coherence of
this light source offers various approaches to radiology.2– 6
Several imaging techniques utilizing coherent light sources,
such as holography and interferometry, have been intensively
studied, and some phase contrast imaging methods have been
announced recently.7–10
In conventional PIV, velocity vectors are extracted by
flow images of tracer particles illuminated with a laser beam.
In x-ray PIV, however, the refraction or Fresnel edge diffraction mechanism of an x-ray beam can be used to improve the
image quality.2– 6 The relative weights of refraction and
Fresnel edge diffraction in x-ray imaging depend on the experimental conditions, the type of specimen, and the information to be extracted.11
II. EDGE ENHANCEMENT BY REFRACTION
An x-ray beam of sufficient coherence can induce the
classic Fresnel edge diffraction pattern in radiological images. In general, the fringe pattern by edge diffraction becomes clearer as the object–detector distance is increased.
The performance of diffraction-based edge detection depends
on several factors such as beam monochromaticity, source
size, and lateral resolution of the detector.11 However, the
details of the diffraction mechanism are beyond the scope of
this paper because refraction-based imaging was mainly used
in this study.
Refraction-based edge enhancement occurs because
specimen regions with different real parts of the refractive
index induce different lateral displacements of a collimated
x-ray beam. Figure 1 shows a schematic diagram of a
refraction-based mechanism of edge enhancement in radiographs. When an object with a tapered edge is illuminated by
a plane-wave x-ray beam, absorption of the x-ray beam by
the object decreases the beam intensity and refraction at the
0021-8979/2003/94(5)/3620/4/$20.00
3620
© 2003 American Institute of Physics
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J. Appl. Phys., Vol. 94, No. 5, 1 September 2003
FIG. 1. Schematic diagram of a refraction-based method of edge enhancement.
edge displaces the beam by a small angle ␣. The angle ␣ is
determined by the slope of the taper at the edge and the real
part of the refractive index of the object. The angular displacement leads to the formation of a highly illuminated area
and a darker area on the detector. This fringe effect enhances
the visibility of the edge in the recorded x-ray image. The
distance A between the dark and bright fringes on the detector depends on the width of the tapered edge. The width B of
each fringe is given by B⬇r 0 ␣ , where r 0 is the distance
between the object and the detector. As indicated by this
relation, the refraction-based edge enhancement becomes
blurred at large r 0 . If r 0 is very small, on the other hand, the
lateral resolution of the fringe on the detector is too small to
identify the edge. Thus, the refraction-based method is effective only over a certain range of object–detector distances. In
contrast to the diffraction method, the refraction method does
not require that the x-ray beam be longitudinally coherent
共monochromatic兲. The refraction-based method therefore depends on the morphology of body to be measured and the
object–detector distance.11
III. EXPERIMENTAL PROCEDURE AND RESULTS
In this study, we fixed the object–detector distance at a
value at which refraction-based edge enhancement occurs
but diffraction-based edge enhancement is not detected. One
of the main motivations for using this approach is that, in
comparison to the diffraction-based method, the refractionbased method can be available without a monochromatic device and this means that we can acquire higher intensity of
x-ray beam.
Although PIV based on x rays is theoretically feasible, it
was not easy to find suitable tracer particles that satisfy the
requirements of both x-ray imaging and PIV. For tracer particles to be suitable for x-ray PIV, they must have two characteristics, including the tendency to closely track the working fluid and to be detectable by x-ray beam with the edge
enhancement. To find particles with suitable characteristics,
we tested several particle types including polystyrene, glass
bead, microcale bubbles as well as polymer and alumina
(Al2 O3 ) microspheres. In this research, we selected microspheres of alumina (Al2 O3 ), a strong absorber of x rays, as
the tracer particles. When an alumina particle is imaged using refraction-based edge detection, the highly illuminated
S. Lee and G. Kim
3621
FIG. 2. Schematic diagram of experimental setup for x-ray PIV measurements.
fringe gets buried in the absorptive area inside the particle
and the dark fringe becomes distinct at the surface of the
particle. With some preliminary testing, we found the optimum object–detector distance for the specific morphology of
alumina microspheres.
The experiments were performed at the ‘‘white beam’’
line 共1B2兲 of the Pohang Light Source. Figure 2 shows a
schematic diagram of the experimental setup used for the
x-ray PIV measurements. X-ray particle images were recorded on a CCD camera after converting the x rays to visible light with a thin CdWO4 scintillator crystal. The lateral
resolution (⌬x) was better than 5 ␮m when the CCD camera
was coupled to a 10⫻ objective lens. Because the x-ray
beam was continuous, we installed a mechanical shutter to
generate double x-ray pulses for the PIV velocity field measurements. A delay generator was used to synchronize the
mechanical shutter and the CCD camera. The time interval
between consecutive images was fixed at 20 ms.
The x-ray PIV technique was applied to a vertical liquid
flow in an opaque Teflon tube with an inner diameter of 750
␮m. The tracer particles 共alumina microspheres兲 had a mean
diameter of 3 ␮m and a density of 3.965 g/cm3 . To match the
specific weight of the alumina particles, glycerin
(1.260 g/cm3 ) was used as the working fluid. The working
fluid seeded with tracer particles was injected into the microtube by a syringe pump at a mean velocity of 0.5 mm/s. The
field of view was about 1.5⫻1.5 mm2 and the spatial resolution was 12.3 ⫻12.3 ␮ m2 . A two-frame cross-correlation
PIV algorithm was applied to each pair of consecutive x-ray
particle images to obtain the corresponding instantaneous velocity field.
Figure 3 shows a typical raw image acquired using the
x-ray imaging technique based on the refraction method. The
object-detector distance was fixed at 30 cm in consideration
of the morphology of the alumina microspheres. The tiny
dark points densely filling the vertical tube indicate the alumina seed particles. The large dark stains and small bright
spots are artifacts caused by flaws on the scintillator surface.
This particle image is suitable for PIV analysis to extract the
instantaneous velocity vector field.
Figure 4 shows the streamwise mean velocity field obtained by ensemble averaging 100 instantaneous velocity
fields. The bright area near the wall indicates low velocity
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3622
J. Appl. Phys., Vol. 94, No. 5, 1 September 2003
S. Lee and G. Kim
FIG. 5. Amassed velocity distribution for circular pipe flow.
FIG. 3. A typical particle image acquired using the x-ray imaging technique.
and the dark area at the tube center indicates high velocity.
The bright spots observed in the ensemble averaged velocity
field are artifacts due to flaws on the scintillator surface.
The velocity data obtained by x-ray PIV contain
amassed flow information in the direction of x-ray propagation, because the x-ray image contains all particles located
inside the pathway of the x-ray beam. Such amassed flow
information gives x-ray PIV the remarkable ability to directly measure amassed volumetric flow information. Thus,
x-ray PIV can be used to measure the volumetric flow rate of
any liquid enclosed within an opaque material, for example
the rate of blood flow in a living organism. For twodimensional or axisymmetric flows, the velocity field information in a cross section of the flow can be obtained using a
mathematical formula derived based on a simple assumption.
The three-dimensional particle displacement data in a volume can be obtained by utilizing a tomography technique in
x-ray PIV.
Figure 5 shows a schematic diagram of the amassed flow
velocity distribution in a circular tube. For laminar flow in a
circular tube installed in the vertical direction, the velocity
distribution can be expressed as follows using the Navier–
Stokes equations and Poiseuille’s law
U共 r 兲⫽
冉
R 2 ⌬p
⫹␳g
4␮ l
冊冋 冉 冊 册
1⫺
r
R
冋 冉 冊册
2
r
R
⫽V max 1⫺
2
,
where R is the radius of circular tube, ␮ is dynamic viscosity
of fluid, ⌬ p is the pressure drop, l is a length along the tube,
␳ is density of fluid, and g is the local acceleration of gravity.
The following amassed velocity distribution can then be obtained from the relationship r 2 ⫽x 2 ⫹y 2 and integration of
the velocity profile.
2
U Amassed共 x 兲 ⫽
冕
冑R 2 ⫺x 2
0
冋 冉 冊 冉 冊册
V max 1⫺
x
R
2
⫺
y
R
2
dy
2 冑R 2 ⫺x 2
冋 冉 冊册
x
2
⫽ V max 1⫺
3
R
2
.
Thus, the amassed velocity profile is only two-thirds of the
theoretical velocity profile for flow in a circular pipe.
Figure 6 shows a typical streamwise mean velocity profile extracted from the mean velocity field data along a horizontal line. The theoretical velocity profile at the center section U(r) and the theoretical amassed velocity profile
U AmTh(x) are included for comparison. The maxima of the
experimental and theoretical amassed velocity profiles
(U AmExp(x) and U AmTh(x)) are put on the same position for
comparison with each other. The amassed velocity profile
obtained using x-ray PIV has a parabolic shape and a magnitude that is about two thirds of the center-sectional velocity
profile, as mentioned above. However, the measured
amassed velocity profile has slightly higher values than the
theoretical profile in the region of large velocity gradient.
This discrepancy seems to be due to the density difference
between the working fluid and the alumina particles. The
effect of the larger gravity of the alumina particles seems to
be pronounced in the near-wall region, where the fluid velocity is slower, even though the gravitational acceleration is
constant across the entire cross section.
FIG. 4. Ensemble-averaged streamwise mean velocity field.
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J. Appl. Phys., Vol. 94, No. 5, 1 September 2003
S. Lee and G. Kim
3623
found to be 30 cm; at this distance the refraction-based edge
enhancement was employed for acquiring a clear x-ray particle image.
The tracer particles used in x-ray PIV should closely
track the working fluid flow and be detectable using the
refraction-based method. In the present work alumina microspheres were selected as the tracer particles. However, the
density of these alumina particles was higher than that of the
working fluid. Despite the difference in density between the
particles and working fluid, we measured the quantitative
velocity field information inside an opaque tube using the
x-ray PIV technique.
X-ray PIV has potential applications in diverse research
areas and can be used as a powerful tool for resolving many
unsolved fluid mechanical problems. One example that
would be particularly well suited to study using x-ray PIV is
blood flow inside living bodies.
FIG. 6. Comparison of streamwise mean velocity profiles: 共—兲 theoretical
center-sectional velocity profile; 共
兲 theoretical amassed velocity profile; 共¯"兲 measured amassed velocity profile.
IV. CONCLUSION
ACKNOWLEDGMENT
The present work was financially supported by POSRIP
共POSTECH Research Initiative Program兲 of POSTECH.
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1
In this study we have devised and begun to explore an
x-ray PIV velocity field measurement technique. The proposed technique can be used to obtain quantitative information on the entire flow field of flows enclosed by opaque
materials. The main contribution of this study is that it establishes the optimum conditions for acquiring good x-ray
particle images from which velocity vectors can be extracted.
We established the refraction-based edge enhancement
method for x-ray particle imaging, conducted experiments to
select the suitable material for the tracer particles, and optimized the object–detector distance for the refraction-based
edge enhancement method and the chosen tracer particles.
The optimal distance between the object and detector was
2
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