Proceedings of 3rd International Workshop on PIV, Santa Barbara, USA, Sep.16-18, 1999
A Comparative Study of the PIV and LDV Measurements on a
Self-induced Sloshing Flow
Tetsuo SAGA, Hui HU, Toshio KOBAYASHI, Shigeki SEGAWA and Nobuyuki TANIGUCHI
Institute of Industrial Science, University of Tokyo, 7-22-1 Roppongi, Tokyo 106, Japan
E-mail: saga@.iis.u-tokyo.ac.jp or huhui@cc.iis.u-tokyo.ac.jp
Masaho NAGOSHI and Taizo HIGASHIYAMA
Fluid Measuring Instrument Division, KANOMAX JAPAN,INC.
3-18-20 Nishishinjyuku, Tokyo160, Japan
Koji OKAMOTO
Nuclear Engineering Research Laboratory, University of Tokyo,
Tokai-mura, Ibaraki, 319-11, Japan
ABSTRACT
Particle Imaging Velocimetry (PIV) and Laser Doppler
Velocimetry (LDV) measurements on a self-induced sloshing
flow in a rectangular tank had been conducted in the present
study. The PIV measurement result was compared with LDV
measurement result quantitatively in order to evaluate the
PIV system. The comparison results show that the PIV and
LDV measurement results agree with each other well in
general for both the mean velocity and turbulence intensity.
The disagreement level of the mean velocity between the PIV
and LDV results found to be within 3% of the target velocity
for PIV parameters selection. Bigger disagreement were
found to concentrate at the high turbulence intensity region.
The space and time resolution difference and the limited
frame number of the PIV result were suggested to be the
main reasons for such disagreement.
INTRODUCTION
As a non-intrusive whole field measuring technique,
Particle Imaging Velocimetry (PIV) can offer many
advantages for the studying of fluid mechanics over other
conventional one-point experimental techniques like Laser
Doppler Velocimetry (LDV) or Hot Wire Anemometer
(FWA). For example, PIV can reveal the global structures in
a two-dimensional or three-dimensional flow field
instantaneously and quantitatively without disturbing the flow,
which are very useful and necessary for the research of flow
mechanism, in particular for the study of unsteady flow.
In order to evaluate the effectiveness and accuracy level of
PIV result, many studies had been conducted based on the
image processing result of artificial images, which were
generated artificially with a pre-set velocity distribution, by
using various PIV image processing methods or algorithms.
By comparison of the velocity distribution obtained through
PIV image processing and the pre-set velocity data of the
artificial images, the accuracy level of the PIV result was
evaluated. Many important results had been got through these
studies. However, it should be noted that the artificial images
used in those researches always have very good image quality,
i.e. much better signal to noise ratio (SNR) than the PIV
images obtained from a real PIV experiment. Besides PIV
image processing, PIV experiment also includes illumination
and image capturing, which may affect the PIV result
accuracy as well. So, the accuracy level can be got in a real
PIV experiment still can not be fully predicted just based on
the PIV image processing result of those artificial images.
In order to evaluate the accuracy level of a PIV system can
be got in a real PIV experiment, a comparative study of PIV
and LDV measurements on a same flow field had been
conducted in the present study. The measurement target flow
is a self-induced sloshing flow field in a rectangular tank (Fig.
1). The free surface of the water in the rectangular tank
oscillated periodically with a constant frequency which is
decided by the eigenvalue of the water in the test tank. The
results of the PIV measurement and LDV measurement were
compared quantitatively to evaluate the PIV measurement.
The compared parameters used in the present study included
the freqency of the self-induced sloshing, the time average
velocity and turbulence intensity, phase average velocity and
turbulence intensity values. The effect of the sample number
of the PIV instantaneous frames and the space resolution of
the PIV images on the accuracy level of the PIV result were
also discussed in the present study.
free surface
inlet
H=160mm
b=20mm
Y
L=110mm
X
outlet
Z
S=150mm
T=50mm
E=60mm
W=300mm
Figure 1. The schematic of the test tank
EXPERIMENT SETUP
1. The target flow and experiment setup
The measurement target flow is a self-induced sloshing
flow field in a rectangular tank. Figure 1 shows the schematic
view of the thin rectangular test tank. Working fluid (water)
flowed horizontally into the test tank and flowed out at a
bottom centered vertical outlet. It was found that under
certain condition of water level and inlet jet velocity, the free
surface of the fluid (water) in the rectangular tank might
oscillate periodically at a constant frequency decided by the
eigenvalue of the fluid in the test tank. This phenomenon was
called as "self-induced sloshing". The characteristics of the
self-induced sloshing had been studied by many researches
(Okamoto et al. 1991, Fukuya et al. 1996, Saeki et al. 1998
and Hu et al. 1999). The excitation of the self-induced
sloshing was considered to be the non-linear interaction
between the jet instability and the sloshing motion.
overflow
head tank
laser sheet
twin Nd:Yag lasers
(15Hz,20mJ/Pulse)
flowmeter
pump
honeycomb sturcture
valve
test section
Synchronizer
lower tank
cross-correlation
CCD Camera
(1008 by 1018)
PC computer
(RAM 1GB,HD 20GB)
Figure 2. The schematic of the experiment setup
Figure 2 shows the experimental setup system used in the
present research. The flow in the test loop was supplied from
a head tank, which was continuously pump-filled from a
lower tank. The water level in the head tank was maintained
in constant by an overflow system in order to eliminate the
effect of the pump vibration on the inlet condition of the test
tank. The flow rate of the loop, which was used to calculate
the representative velocity and Reynolds numbers, was
measured by a flow meter. A convergent unit and Honeycomb
structures were installed in the upstream of the inlet of the
test tank to insure the uniform flow entrance. The flow rate
and the water level of the free surface in the test tank can be
adjustable by changing the position of the valves installed in
the flow loop.
During the experiment, the water level in the test tank was
set at about H=160mm. The flow rate of the test loop was
about 20 liter/min, which corresponded to the average
velocity at the inlet of the test tank being about 0.333 m/s,
and Reynolds number about 6,700 based on the height of the
inlet (b=20mm). Since the test tank was designed to have the
flow field in the test tank to be two dimensional, our
measurement result showed that the flow field in the test tank
was almost two-dimensional except the regions near the two
walls. The comparative measurement of the PIV and LDV
were conducted at the middle section of the test tank
(Z=25mm section) in the present study.
2.
PIV system
For the PIV measurement, twin pulsed Nd:YAG Lasers
were used to supply pulsed laser sheet (thickness of the sheet
is about 1.0 mm) with the frequency of 7.5 Hz and power of
20 mJ/pulse to illuminated the measured flow field.
Polystyrene particles (diameter of the particles is about 20-50
μm, density is 1.02kg/l) were used as PIV tracers in the flow
field. A 1008 by 1016 pixels Cross-Correlation CCD array
camera (PIVCAM 10-30) was used to capture the images.
The twin Nd:YAG Lasers and the CCD camera were
controlled by a Synchronizer Control System. The PIV
images captured by the CCD camera were digitized by an
image processing board, then transferred to a workstation
(host computer, CPU450MHz, RAM 1024MB, HD20GB) for
image processing and displayed on a PC monitor.
In the present PIV measurement, two kinds of the PIV
images were captured with different space resolution. One is
the 0.16mm/pixel (high resolution) and another is
0.32mm/pixel (low resolution). In the present study, rather
than tracking individual particle, the cross correlation method
(Willert et al., 1991) was used to obtain the average
displacement of the ensemble particles. The images were
divided into 32 by 32 pixel interrogation windows, and 50%
overlap grids were employed for the PIV image processing.
The time interviel between the two pulses was set at 2-4ms to
have the average displacement of the particles in the inlet jet
is about 4 to 6 pixels. The post-processing procedures which
including sub-pixel interpolation (Hu et al., 1998) and
velocity outliner deletion (Westerweel, 1994) were used to
improve the accuracy of the PIV result.
Since the cross-correlation method was used for PIV image
processing, the obtained velocity is the average velocity of
the particles in the interrogation window. So, the space
resolution ability should be the size of the interrogation
windows. Therefore the space resolution of the PIV
measurement is 5mm×5mm×1mm for the high resolution
case and 10mm×10mm×1mm for the low resolution case
by using 32 by 32 pixel interrogation windows. Since the
frequency of the pulsed Nd:Yag lasers were set at 7.5 Hz, the
time resolution of the present PIV measurement is 3.75Hz
according to the Nyquist critical principle.
3. LDV system
The LDV system used in the present study was composed
by an Argon Laser (1.5W), a LDV optical unit (TSI TRCF2),
a signal processing system (TSI IFA750) and a Synchronizer
Control System (TSI Datalink DL4). Polystyrene particles
with the diameter of 1μm and density of 1.02 kg/l were used
as tracers for the LDV measurement. 30,000 data obtained at
about 30 seconds were used for the time average velocity and
turbulence intensity calculation at every point. The space
resolution of the LDV system is about 65.3μm (volume
diameter)×0.68mm (volume lenght). Since the sample rate
of the LDV measurement is set as 1000Hz, the time
resolution of the LDV measurement is 500 Hz according to
the Nyquist critical principle.
RESULTS AND DISCUSSIONS
1. Oscillation frequency of the self-induced sloshing
Figure 3 shows the oscillation of the free surface of the
water in the test tank with time at three positions, i. e., left
side (inlet side), center and left side of the test tank. The
frequency of the self-induced sloshing can be calculated from
these signals, which is 1.6Hz.
According to the research of Fukaya et al.(1996), the
self-induced sloshing mode of the present study is 1st mode.
Okamoto et al. (1991) had suggested that the frequency of the
self-induced sloshing equal to the eigenvalue of the water in
the test tank, which can be expressed as:
1 nπg
nπH
(1)
tanh(
)
2π W
W
By using above equation, the 1st mode eigenvalue of the
water in the test tank for the present study case can be
calculated, which is 1.56Hz. The difference between the
frequency of the self-induced sloshing measured by present
study (f=1.6Hz) and the 1st mode eigenvalue of the water in
the test tank is within the 3% range, which verified the
propose of Okamoto et al.(1991).
fn=
m iddle
right side
0.10
0
0.5
1
1.5
tim e (s)
2
2.5
3
Y mm
Spanwise Vorticity ( Z-direction )
-30.00 -24.00 -18.00 -12.00 -6.00
0.00
6.00
1.6
0.08
Figure 3. The oscillating water level of the free surface
200
0.09
Power Spectrum
Water level (mm
left side
166
165
164
163
162
161
160
159
158
157
156
Figure 4 shows the two typical instantaneous PIV velocity
fields. 1000 frames of such instantaneous velocity fields were
captured in the present PIV measurement with the rate of
7.5Hz. Besides the two large vortices at the right side and left
lower corner of the test tank (which are almost steady
vortices), a smaller vortex (which is unsteady) also can be
found in the flow field, which shed from the inlet plane jet.
The whole flow pattern in the test tank, such as the path of
the inlet plane jet to the oulet, the size of the two steady
vortices, and the flow direction at the exit of the test tank,
changed very drastically with the evolution of this unsteady
vortex. By using these instantaneous velocity fields, the
power spectrum of the velocity can be calculated through
FFT transformation, which was shown on the Figure 5(a).
The power spectrum of the velocity at the same point by
LDV measurement was shown on Figure 5(b). It can be seen
that both PIV and LDV measurements can identify the
oscillation frequency of the self-induced sloshing well with
an obvious peak at the 1.6 Hz in the power spectrum profiles.
0.07
0.06
0.05
0.04
0.03
0.02
12.00 18.00 24.00 30.00
0.01
150
0.00
Re =6,700
0.00
Uin = 0.33 m/s
100
1.00
2.00
Frequency (H z)
3.00
4.00
a. PIV result
50
U out
0
-50
-50
0
50
100
X mm
150
200
250
300
a. t=t0
Spanwise Vorticity ( Z-direction )
Y mm
200
-30.00 -24.00 -18.00 -12.00 -6.00
0.00
6.00
12.00 18.00 24.00 30.00
150
Re =6,700
b. LDV result
Figure 5. The power spectrum of PIV and LDV
measurements at point (X=100mm, Y=110mm, Z=25mm)
Uin = 0.33 m/s
100
50
U out
0
-50
-50
0
50
100
150
X mm
200
250
300
b. t=t0+2.0/7.5
Figure 4. Two typical PIV instantanous velocity fields
2. Time average results
As mentioned above, 1000 frames of the instantaneous
PIV velocity frames obtained by the PIV system at the rate of
7.5 Hz and 30,000 samples at each points got by LDV system
at the data rate of 1000Hz were used to calculate the time
average values of the flow field.
Figure 6 shows the time avevrage velocity fields and
turbulence intensity distributions of PIV and LDV
measurement results. From the figures it can be seen that
only two large-scale vortices can be found at the right side
and the left lower corner of the test tank from the time
average result. The unsteady vortex revealed in the above
instantaneous flow fields, which shed periodically from the
inlet plane jet, cannot be found in the time average results.
However, the high turbulence intensity region can be found
along the shedding path of the unsteady vortex.
200
0.5 m/s
Turbulent Intensity
0.1491
0.1409
0.1327
0.1245
0.1163
0.1081
0.0999
0.0918
0.0836
0.0754
0.0672
0.0590
0.0508
0.0426
0.0344
0.0262
Y mm
150
100
50
0
0
100
200
some local disagreement (always in the high shear region)
between the PIV and LDV result can also be found in the
profiles. This may be explained by that since the PIV and
LDV measurements have different space and time resolution,
the disagreement between them was expected to exist,
especially in the high intensity regions where the effect of the
resolution will be more serious. As the resolution of the PIV
images improving, this disagreement is expected to be
decreased, which can be verified from the figure 8.
It should also be noted that the disagreement between the
PIV and LDV results is more serious in the turbulent velocity
intensity (STD(u) and STD(v)) profiles (Fig.7(b)) than that in
the mean velocity (U and V) profiles (Fig.7(a)). This may be
explained by that, according to the research of Ullum et al.
(1997), the necessary sampling number to calculate the mean
turbulence intensity should be the square of the number to
calculate the mean velocity in order to get the same level of
the standard deviation. So, the standard deviation by using
the same sample number (1000 instantaneous velocity fields)
to calculate the time average turbulence intensity was
expected to be bigger than that to calculate the time average
velocity.
300
X mm
0.4
a. LDV result
Turbulent Intensity
0.1274
0.1194
0.1114
0.1033
0.0953
0.0873
0.0792
0.0712
0.0632
0.0551
0.0471
0.0391
0.0310
0.0230
0.0150
0.0069
Y mm
150
100
50
0
100
200
300
X mm
b. PIV measurement
Figure 6. Time average results by PIV and LDV
measurementes
It can also be seen that the flow pattern in the test tank
revealed by PIV and LDV measurement is similar with each
other very well. In order to give a more quantitatively
comparison of the PIV and LDV measurement results, the
time average velocity and turbulence intensity of the PIV and
LDV measurements along the inlet central line of the test
tank were shown on Figure 7.
Since the parameter selection of the present PIV
measurement was based on the velocity of the inlet jet flow
(target velocity), which is about 0.4m/s, the 3% region of the
target velocity (0.4m/s) was also shown on the Fig.7(a) for
the PIV measurement results. It can be seen that, the PIV
result agreed with LDV result well in general for both the
time average velocity and turbulence intensity. The
disagreement of the PIV and LDV results for the time
average velocity is within 3% of the target velocity. However,
Velocity (m/s
0.5 m/s
0.2
0.1
0
-0.1
-0.2
0
50
100
150
X (m m )
200
250
300
250
300
(a). mean velocity
0.14
Turbulence intensity (m
200
0
U -piv
V -piv
U -ldv
V -ldv
0.3
0.12
STD (u)-piv
0.10
STD (v)-piv
STD (u)-ldv
0.08
STD (v)-ldv
0.06
0.04
0.02
0.00
0
50
100
150
X (m m )
200
(b). Turbulence intensity
Figure 7. The comparison of the time average values of PIV
and LDV measurement along the inlet central line
3 The effect of the PIV image resolution
As mentioned above, two resolution levels of the PIV
images had been captured in the present study. Figure 8
shows the disagreement distributions of the LDV result and
PIV results by using these two kinds of images with different
space resolution.
From the figures, It can be seen that the average
disagreement level of LDV and PIV in the whloe flow field is
within 3% of the target velocity. The bigger disagrement
200
LDV-PIV
0.0500
0.0475
0.0450
0.0425
0.0400
0.0375
0.0350
0.0325
0.0300
0.0275
0.0250
0.0225
0.0200
0.0175
0.0150
0.0125
0.0100
0.0075
0.0050
0.0025
0.0000
O.1 m/s
Y mm
150
100
50
0
0
100
200
as the PIV image resolution increasing, the disagreement
between the LDV and PIV measurement decreasd
200
LDV-PIV
0.0500
0.0475
0.0450
0.0425
0.0400
0.0375
0.0350
0.0325
0.0300
0.0275
0.0250
0.0225
0.0200
0.0175
0.0150
0.0125
0.0100
0.0075
0.0050
0.0025
0.0000
O.1 m/s
150
Y mm
between LDV and PIV results were found to concentrate at
the high turbulence intensity region. It also can be seen that
100
50
0
300
0
100
X mm
200
300
X mm
a. low resolution (0.32 mm/pix)
b. high resolution (0.16 mm/pix)
Figure 8 The effect of the image resolution on the PIV measurement results.
Spanwise Vorticity ( Z-direction )
Spanwise Vorticity ( Z-direction )
-25.00 -20.00 -15.00 -10.00 -5.00
0.00
5.00
Y mm
200
Y mm
200
10.00 15.00 20.00 25.00
water free surface
150
-25.00 -20.00 -15.00 -10.00 -5.00
0.00
5.00
10.00 15.00 20.00 25.00
water free surface
150
Re =6,700
Re =6,700
Uin = 0.33 m/s
Uin = 0.33 m/s
50
50
0
0
-50
-50
0
50
100
U out
100
U out
100
X mm
150
200
250
300
-50
-50
0
(a). situation 1 (θ=0)
50
5.00
Y mm
Y mm
0.00
200
250
300
Spanwise Vorticity ( Z-direction )
200
-25.00 -20.00 -15.00 -10.00 -5.00
X mm
150
(b). situation 2 (θ=π/2)
Spanwise Vorticity ( Z-direction )
200
100
10.00 15.00 20.00 25.00
water free surface
150
-25.00 -20.00 -15.00 -10.00 -5.00
0.00
5.00
10.00 15.00 20.00 25.00
water free surface
150
Re =6,700
Re =6,700
Uin = 0.33 m/s
Uin = 0.33 m/s
50
50
0
0
-50
-50
0
50
100
150
U out
100
U out
100
X mm
200
(c). situation 3 (θ=π)
250
300
-50
-50
0
50
100
150
X mm
200
(d). situation 4 (θ=3π/2)
Figure 9. The phase average flow field of PIV result
250
300
CONCLUSIONS
A comparative study of Particle Imaging Velocimetry
(PIV) and Laser Doppler Velocimetry (LDV) measurements
on a self-induced sloshing flow in a rectangular tank had
been conducted in the present study. The PIV measurement
result was compared with LDV measurement result
quantitatively in order to evaluate the PIV system. The
comparison results show that the PIV and LDV results agree
with each other well in general for both the mean velocity
and turbulence intensity. The disagreement level of the mean
velocity between the PIV and LDV results is within 3% of
the target velocity. Bigger disagreement regions were found
to concentrate at the high turbulence intensity region. The
space and time resolution difference and the limited frame
number of the PIV result were suggested to be the main
reasons for such disagreement.
0.5
Velocity (m/s
0.4
U -P IV
V -P IV
U -LD V
V -LD V
0.3
0.2
0.1
0
-0.1
-0.2
0
50
100
150
X (m m )
200
250
300
a. Phase average mean velocity
0.09
Velocity iNtensity (m
4. Phase average results
Since the free surface of the water in the test tank
oscillated periodically with frequency of 1.6Hz, the phase
average measurement by using PIV and LDV had also been
conducted in the present research. For the phase average
measurement, the free surface water level at the left side
(inlet side) was detected by a water-level detecting sensor,
which can send a signal to the Synchronizer Control System
to trigger the laser pulses and CCD camera. The phase
average results in 250 cycle of self-induced sloshing
ossilation at four phase angles ( θ = 0 , π/2, π and 3π/2)
were shown on Figure 9. The free surface water levels at the
left side (inlet side) of the test tank were at its highest
position, middle level (the free surface level is decreasing),
lowest position and middle level (the free surface level is
increasing) corresponding to these four phase angles.
Unlike the above time average result which can just reveal
two steady vortices in the flow field, the unsteady vortices
can also be visulized clearly in the flow field from the phase
average measurement results. Besides the two steady vortices
at the left lower corner and right side of the test tank, the
unsteady vortex was found to change its position with the
changing of the phase angle. When the phase angle increased
from 0 toπ, i.e., the free surface water level at the left side of
the test tank decreased from its highest position to its lowest
position (from Fig.9(a), Fig.9(b) to Fig.9(c)). The unsteady
vortex shed from the inlet plane jet and moved downstream.
When the phase angle increased from π to 2π, i.e, the free
surface water level at the left side of the test tank began to
increased from its lowerst position to its highest position
(from Fig. 9(c), Fig. 9(d) to Fig. 9(a)). The unsteady vortex
was engulfed by the large steady vortex at the right side of
the test tank, and another new vortex was found to roll up
from the inlet of the test tank. Then, another new self-induced
sloshing cycle began.
Figure 10 shows the phase average velocity and turbulence
intensity of the PIV and LDV measurement results along the
inlet central line of the test tank at the phase angle of π/2.
Just as the time average results shown on Fig.7, the PIV and
LDV results agreed with each other well in general. For The
phase average velocity, the disagreement of PIV and LDV
was also found within 3% of the target velocity. However,
the disagreement of the turbulence intensity (in the high shear
region) between the PIV and LDV results was found to be
more serious than its time average counterpart (Fig.7(b)),
these may becasue that the fewer sample number for the
phase average (250 frames) than that for the time average
(1000 frames).
0.08
STD (U )-P IV
STD (V )-P IV
STD (U )-LD V
STD (V )-LD V
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
0
50
100
150
X (m m )
200
250
300
b. Phase average turbulence intensity
Figure.10 The phase average results along the inlet central
line of the PIV and LDV measueremnt (phase angleπ/2)
REFERENCE
Fukaya, M. Madarame, H. and Okamoto, K., (1996)
Growth Mechanism of Self-Induced Sloshing Caused by
Jet in Rectangular Tank.Trans. of JSME, (B), Vol.62,
No.599. pp64 -71
Hu, H., Saga, T., Kobayashi, T., Okamoto, K. and
Taniguchi, N. (1998). Evaluation of the Cross
Correlation Method by Using PIV Standard Images.
Journal of Visualization, Vol.1, No.1, pp87-94.
Hu, H., Kobayashi T., Saga, T., Segawa S., Taniguchi, S.
Nagoshi M. and Okamoto K. (1999) A PIV Study on
the Self-induced Sloshing in a Tank with Circulating
Flow. Processing of The 2nd Pacific Symposium on
Flow Visualization and Image Processing.
Okamoto, K., Madrarame, H. and Hagiwara, T. (1991).
Self-induced Oscillation of Free Surface in a Tank with
Circulating Flow. C416/092, IMechE, pp539-545
Saeki, S., Madarame, H., Okamoto, K, and Tanaka, N.,
1998. Numerical Study on the Growth Mechanism of
Self-Induced Sloshing Caused by Horizontal Plane Jet
FEDSM98-5208, ASME FED Summer Meeting.
Ullum, U., Schmidt, J. J., Larsen P. S., and McClusky, D.
R. (1997) Statistical Analysis And Accuracy of PIV Data.
Proc. of 2nd Int. Workshop on PIV.
Willert, C. E. and Gharib, M. (1991) Digital Particle Image
Velocimetry. Experiments in Fluids, Vol.l0, ppl8l-l99
Westerweel, J. (1994) "Efficient Detection of Spurious
Vectors in Particle Image Velocimetry Data", Exp. In
Fluids, Vol.16, pp236-247.