Proceeding of PSFVIP-2
May 16-19, 1999, Honolulu, USA
PF152
A PIV Study on the Self-induced Sloshing
in a Tank with Circulating Flow
Hu Hui, Toshio Kobayashi, Tetsuo Saga, Shigeki Segawa and Nobuyuki Taniguchi
Institute of Industrial Science, University of Tokyo, 7-22-1 Roppongi, Tokyo 106, Japan
E-mail: huhui@cc.iis.u-tokyo.ac.jp
Masaho Nagoshi
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
The self-induced sloshing in a rectangular tank with circulating flow had been investigated
experimentally by using Particle Imaging Velocimetry (PIV) technique. The instantaneous
flow fields, time average values and phase average results of the PIV measurement were
used to analyze the mechanism of the self-induced sloshing of the water free surface in the
test tank. Besides the two steady vortices in the left lower corner and right side of the test
tank reported by Okamoto et al. (1993a), a new unsteady vortex was found in the test tank
shedding periodically from the inlet plane jet. The shedding frequency of this unsteady
vortex was found to be the frequency of the self-induced sloshing, which also equals the
eigenvalue of the water in the test tank. The flow parttern in the test tank changes
drastically with the periodic shedding of this unsteady vortex. Based on the experimental
result, resonated oscillation was suggested to be the mechanism of the self-induced
sloshing, and the instability of the inlet plane jet was conjectured to be the excitation
source of the self-induced sloshing.
Keyword: self-induced sloshing, vortex shedding, resonated oscillation, and PIV technique
INTRODUCTION
Self-induced sloshing is a natural oscillation phenomenon that had been paid great attention by many
researchers in the fields of civil engineering, petroleum industry and nuclear energy engineering. For
example, in the Liquid Metal Fast Breeder Reactor (LMFBR), which is one of the major energy plants in
the near future, the self-induced sloshing of the sodium coolant may occur in the reactor vessel. Such selfinduced sloshing can result in high thermal stresses on the vessel walls, which may do severe damage to the
vessel structures (Okamoto et al. 1998). So, the mechanism of the self-induced sloshing should be
understood clearly in order to do an optimum safety design to prevent the self-induced sloshing of the
sodium coolant in the reactor vessel.
Since the first systemical research on the self-induced sloshing in a rectangular tank reported by
Okamoto et al. (1991), several investigations on the self-induced sloshing in a rectangular tank with
circulating flow had been conducted experimentally and numerically in the past ten years. Okamoto et al.
(1991) reported that the self-induced sloshing was found to occur in a certain region of the flow rate and
water level in a rectangular tank, and the frequency of the free surface sloshing equaled to the eigenvalue of
the water in the test tank. Based on the superposition of the steady circulating flow in the test tank being
represented by an ideal flow with a vortex, Madarame et al. (1992) proposed that the oscillation energy of
the sloshing be supplied by pressure fluctuations caused by the interaction between the circulating flow and
the sloshing motion. Fukaya et al. (1996) reported that two kinds of sloshing mode were observed under the
certain geometrical condition of a rectangular tank, and proposed that the self-induced sloshing be caused
by the interaction of the plane jet flow with the free surface.
Numerical simulation of the self-induced sloshing was firstly carried out by Takizawa et al. (1992a).
They solved two-dimensional Navier-Stokes equations with Physical Component Boundary Fitted
Coordinate (PCBFC) (Takizawa et al. 1992b). Based on the analyzing of their numerical result, they
suggested that the oscillation energy of the self-induced sloshing be supplied by the surface potential,
which was varied by the secondary flow due to the flow circulating. The recent work of Saeki et al.(1997,
1998) used a Boundary Fitted Coordinate (BFC) method with height function to conduct two-dimensional
numerical simulation. They reported that their numerical result agreed with an experiment result very well
and also suggested that the self-induced sloshing was mainly dependent on the inlet jet fluctuation.
Although many important results had been got through these previous investigations, much work still
needs to be done to understand the fluid dynamic mechanism of the self-induced sloshing more clearly.
Such as, the evolution of the vortices and the turbulent structures in the test tank were not fully researched
yet. Meanwhile, most of the previous experimental researches were mainly based on the qualitative flow
visualization. Although a primary PIV measurement had been conducted by Okamoto et al. (1993b), the
resolution of their measurement was not fine enough to reveal small-scale vortices in the test tank due to
the limitation of their PIV hardware. In the present study, a high-resolution PIV system was used to study
the self-induced sloshing in a rectangular tank instantaneously. By using the instantaneous PIV results,
time-average values and the phase-average result of the PIV measurement, the evolution of the vortices,
and the turbulent structures in the test tank were studied, and then, the mechanism of the self-induced
sloshing was suggested based on the PIV measurement result.
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 520MB,HD 12GB)
Figure 1. The schematic of the experiment setup
EXPERIMENT SETUP
Figure 1 shows the experimental setup 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. Honeycomb structures and a
convergent section were installed in the upstream of the inlet of the test tank to insure the uniform flow
entrance. A valve was installed at the downstream of the test tank exit to adjust the water level of the free
surface in the test tank.
Figure 2 shows the schematic view of the thin rectangular test tank. Water flowed horizontally into the
test tank and flowed out at a bottom centered vertical outlet. During the experiment, the water level in the
test tank was 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 let the flow field in the test
tank to be two dimensional (our measurement result also showed that the flow field in the test tank was
almost two dimensional along the Z direction except the regions near the two walls), PIV measurement was
just conducted at the middle section of the test tank (Z=25mm section) in the present study.
free surface
inlet
H=160mm
b=20mm
Y
L=110mm
X
outlet
Z
T=50mm
S=150mm
E=60mm
W=300mm
Figure 2. The schematic of the test tank
The pulsed laser sheet (thickness of the sheet is about 1.5 mm and the life per pulse is 6ns) used for PIV
measurement was supplied by a Twin Nd:YAG Laser with the frequency of 15 Hz and power of 20
mJ/pulse. Polystyrene particles (diameter of the particles is about 20-50 m , density is 1.02) were used as
PIV tracers in the flow field. A 1008 by 1018 pixels Cross-Correlation CCD array camera (PIVCAM 1030) was used to capture the images. The Twin Nd:YAG Laser 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 PC computer (host computer, RAM 512MB, HD12GB) for image
processing and displayed on a PC monitor.
To obtain fluid velocities by using PIV technique, two or more images of seeded flow fields are captured
at successive points in time, and comparison of these images allows the velocity fields to be constructed. 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
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.
RESULTS AND DISCUSSIONS
1.Oscillation frequency of the self-induced sloshing
Figure 3 shows the oscillation of the free surface 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 about 1.6Hz.
According to the definition 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:
fn=
1
2π
nπg
nπH
tanh(
)
W
W
Water level (mm)
left side
middle
right side
166
165
164
163
162
161
160
159
158
157
156
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
time (s)
Figure 3. The oscillating water level of the free surface
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. So, the difference between the frequency of the self-induced sloshing
(f=1.6Hz) measured in present study 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) once again.
2.Instantaneous flow field
As mentioned above, since the frequency of the illumination pulse supplied by the Nd:YAG Laser was
settled as 15 Hz, the instantaneous PIV velocity field can be got at the rate of 7.5Hz (two pulses for one
velocity field). According to the above measurement result, the frequency of the self-induced sloshing is
1.6Hz for the present study condition. This means about 5 instantaneous velocity fields can be obtained for
every cycle of the self-induced sloshing by using present PIV system. Figure 4 shows the 6 continuous
instantaneous PIV measurement results. The time interval between the Fig. 4(a) and Fig.4(f) is about one
period of the self-induced sloshing. The evolutions of the vortices and turbulent structures in the test tank
can be seen clearly from these instantaneous flow fields. It can be seen that, beside the two large vortices at
the right side and left lower corner of the test tank (which are almost steady vortices), there is another
smaller vortex (which is unsteady) shedding from the inlet plane jet. Since there is only one unsteady
vortex shedding can be found for one cycle of the self-induced sloshing, the shedding frequency of this
smaller unsteady vortex is equal to the frequency of the self-induced sloshing. The whole flow pattern in
the test tank, such as the form of the inlet plane jet, 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.
Figure 5 shows two typical power spectrum profiles of the velocity (u and v components) in the test
tank obtained by PIV measurement. Since the PIV instantaneous flow field was got at the rate of 7.5Hz, the
spectrum range of the PIV measurement result is less than 3.75 Hz. From the figure, it can be seen that
there is an obvious peak at the frequency value of 1.6Hz in the power spectrum profiles for both ucomponent and v-component. This means that the velocity field in the test tank was affected mainly by the
periodic shedding of the unsteady vortex.
3. Time average result
In the present study, time average value of the PIV measurement result was also used to research the
self-induced sloshing phenomena. 1000 PIV instantaneous velocity fields were used to calculate the mean
values of the velocity field and turbulent intensity field. Since the PIV instantaneous velocity fields were
got at the rate of 7.5Hz by using the present PIV system, the sampling time interval for getting 1000
instantaneous PIV velocity fields was about 130 seconds, and it was about the life of 210 cycles of the selfinduced sloshing.
-30.00 -24.00 -18.00 -12.00 -6.00
0.00
6.00
12.00 18.00 24.00 30.00
150
Spanwise Vorticity ( Z-direction )
Y mm
200
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
Re =6,700
Uin = 0.33 m/s
Uin = 0.33 m/s
50
50
0
0
-50
-50
0
(a).
100
X mm
150
200
250
-50
-50
300
0
at time t=T0
(b).
-30.00 -24.00 -18.00 -12.00 -6.00
0.00
6.00
12.00 18.00 24.00 30.00
150
50
100
X mm
150
200
250
300
at time t=T0+1/7.5 s
Spanwise Vorticity ( Z-direction )
Y mm
200
Spanwise Vorticity ( Z-direction )
Y mm
200
50
U out
100
U out
100
-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
Re =6,700
Uin = 0.33 m/s
Uin = 0.33 m/s
50
50
0
0
-50
-50
0
(c).
100
X mm
150
200
250
-50
-50
300
0
at time t=T0+2/7.5 s
200
0.00
6.00
100
X mm
150
200
250
300
12.00 18.00 24.00 30.00
150
Spanwise Vorticity ( Z-direction )
Y mm
-30.00 -24.00 -18.00 -12.00 -6.00
50
(d). at time t=T0+3/7.5s
Spanwise Vorticity ( Z-direction )
Y mm
200
50
U out
100
U out
100
-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
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
250
-50
-50
300
(e). at time t=T0+4/7.5 s
0
50
100
150
X mm
200
250
(f). at time t=T0+5/7.5 s (new cycle )
Figure 4. The instantaneous velocity and spanwise voriticity distributions
300
Power Spectrum
0 .1 0
1 .6
0 .0 8
0 .0 6
0 .0 4
0 .0 2
0 .0 0
0 .0 0
0 .5 0
1 .0 0
1 .5 0
2 .0 0
2 .5 0
Freq u en c y (H z)
3 .0 0
3 .5 0
4 .0 0
3.00
3.5 0
4 .00
Power Spectrum
(a). u-component
0.0 4
0.0 3
0.0 3
0.0 2
1 .6
0.0 2
0.0 1
0.0 1
0.0 0
0.00
0.5 0
1 .00
1.5 0
2.00
2.5 0
Frequ en cy (H z)
(b). v-component
Figure 5. The power spectrum of the velocity at point (X=100mm,Y=100mm, Z=25mm) by using PIV
200
200
0.5 m/s
100
50
0
100
200
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
150
Y mm
Y mm
150
0
0.5 m/s
VELOCITY
0.3896
0.3639
0.3381
0.3124
0.2866
0.2609
0.2352
0.2094
0.1837
0.1579
0.1322
0.1065
0.0807
0.0550
0.0292
0.0035
100
50
0
300
0
X mm
100
200
300
X mm
(a). mean velocity
(b). Turbulent intensity
Figure 6. The time average flow field of the PIV result
Figure 6 shows the time average result of the flow field in the test tank, which included the mean
velocity field (Fig.6(a)) and the mean turbulent intensity field (Fig.6(b)). The mean velocity (Ui,j and Vi,j )
and the mean turbulent intensity Tij shown on these figures were defined as:
N v
N u
Vi , j = ∑ i , j ,t
U i , j = ∑ i , j ,t
t =1 N
t =1 N
N
Ti , j =
∑ (u
’2
2
i, j , t
i, j, t
)
t =1
N
N
=
+ v’
∑ (u
t =1
N
i, j, t
− U i , j ) 2 + ∑ (vi , j , t − Vi , j ) 2
i =1
N
In which N=1000, ui,j,t and vi,j,t are the instantaneous velocities in the X and Y direction, while u’i,j,t
and v’i,j,t are the instantaneous fluctuating components.
From the figures it can be seen that, just as the results reported by Okamoto et al.(1993b), only two
steady 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 field, which shed periodically from
the inlet plane jet, cannot be found in the time average results. However, the high turbulent intensity region
can be found along the shedding path of the unsteady vortex.
In order to verify the present PIV measurement results, the LDV measurement had also been
conducted along the central lines of the inlet and outlet of the test tank. The comparison of the PIV and
LDV measurement result was shown in Figure 7. In general, the PIV measurement result agrees with the
LDV result well for both the mean velocity (U and V) and mean turbulent intensity (STD(u)and STD(v)).
However, 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 the fact that, since the cross-correlation method was
used in the present study to do PIV image processing, the velocity field got by PIV measurement is the
average velocity of the ensemble particles in interrogation windows. So, the disagreement was expected to
exist between the LDV and PIV measurement, especially in the high shear region. The gap between the PIV
and LDV results is smaller in the mean velocity (U and V) profiles than that in the mean turbulent intensity
(STD(u) and STD(v)) profiles. This may be explained by the following fact: according to the research of
Ullum et al. (1997), the necessary sampling number to calculate the mean turbulent intensity should be the
square of the number to calculate the mean velocity in order to get the same level of the standard deviation
error. So, the standard deviation error by using the same sample number (1000 instantaneous velocity
fields) to calculate the mean turbulent intensity was expected to be bigger than that to calculate the mean
velocity filed.
0.14
0.5
Velocity (m/s)
Turbulent intensity (m/s)
U-piv
0.4
V-piv
0.3
U-ldv
0.2
V-ldv
0.1
0
-0.1
-0.2
0.12
STD(u)-piv
0.10
STD(v)-piv
0.08
STD(u)-ldv
0.06
STD(v)-ldv
0.04
0.02
0.00
0
50
100
150
200
250
300
0
50
100
150
X (mm)
200
250
300
X (mm)
(a). along the inlet central line (Y=110mm, Z=25 mm)
0.12
0.2
U-piv
V-piv
U-ldv
V-ldv
0.1
0.05
STD(u)-piv
Turbulent Intensity (m/s)
Velocity (m/s)
0.15
0
-0.05
-0.1
-0.15
-0.2
0.10
STD(v)-piv
STD(u)-ldv
0.08
STD(v)-ldv
0.06
0.04
0.02
0.00
0
20
40
60
80
100
120
0
140
20
40
60
80
100
120
Y (mm)
Y (mm)
(b). along the outlet central line (X=150mm, Z=25 mm)
Figure 7. The comparison of the PIV and LDV results
140
4. Phase average result
Since the self-induced sloshing oscillated periodically with a frequency of 1.6Hz, the phase average
measurement had also been conducted in the present research. During the measurement, the free surface
water level at the left side (inlet side) was detected by a water-level detecting system, which can sent a
signal to the Synchronizer Control System to trigger the laser pulses and CCD camera. The phase average
results shown on Figure 8 were obtained by the average of the 250 instantanous velocity fields at four
phase angles ( θ = 0 , π , π and 3π ). The free surface water levels at the left side (inlet side) of the test
2
2
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 phase angles, respectively.
0.5 m/s
0.5 m/s
water surface
200
200
VELOCITY
0.4236
0.3958
0.3679
0.3400
0.3122
0.2843
0.2564
0.2286
0.2007
0.1728
0.1450
0.1171
0.0892
0.0614
0.0335
0.0056
100
50
0
0
100
200
VELOCITY
0.4308
0.4024
0.3739
0.3455
0.3171
0.2886
0.2602
0.2318
0.2033
0.1749
0.1465
0.1180
0.0896
0.0612
0.0327
0.0043
150
Y mm
Y mm
150
water surface
100
50
0
300
0
100
X mm
(a). situation 1 ( θ =0)
(b). situation 2 ( θ =
0.5 m/s
200
200
VELOCITY
0.3870
0.3615
0.3361
0.3106
0.2851
0.2597
0.2342
0.2087
0.1833
0.1578
0.1324
0.1069
0.0814
0.0560
0.0305
0.0051
π
)
2
100
50
0
200
water surface
VELOCITY
0.3931
0.3671
0.3412
0.3152
0.2893
0.2633
0.2374
0.2114
0.1855
0.1595
0.1335
0.1076
0.0816
0.0557
0.0297
0.0038
150
Y mm
Y mm
150
100
300
0.5 m/s
water surface
0
200
X mm
100
50
0
300
0
100
X mm
200
300
X mm
(c). situation 3 ( θ = π )
(d). situation 4 ( θ =
3π
)
2
Figure 8. The phase average flow field of PIV result
Unlike the above time average result which can just reveal two steady vortices in the flow field, the
unsteady vortices can also be found clearly in the flow field from the phase average measurement result.
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 change of the phase angle.
When the phase angle increased from 0 to π , 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.8(a), Fig.8(b) to Fig.8(c)); the
unsteady vortex shed from the inlet plane jet and moved downstream. When the phase angle increased from
π to 2 π , 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. 8(c), Fig. 8(d) to Fig. 8(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 rollen up from
the inlet of the test tank. Then, another new self-induced sloshing cycle began.
5.The mechanism of the self-induced sloshing
As mentioned above, Okamoto et al. (1991) had proposed that the frequency of the self-induced
sloshing always equaled to the eigenvalue of the water in the test tank, and the measurement result of the
present research also verified this conclusion. That means the self-induced sloshing in the test tank has a
very close relationship with the oscillation characteristics of the water in the test tank. Since the resonated
oscillation just vibrated with the frequency decided by the eigenvalue of the oscillating body, the
"resonance model" was conjectured in the present paper to be the reason for the self-induced sloshing in the
test tank.
It was well known that there are two necessary factors for the resonated oscillation. The first is
excitation source and the second is that the frequency of the excitation should be coupled with the
eigenvalue of the oscillating body. From the above PIV measurement result, it can be seen that during the
self-induced sloshing of the water free surface, the periodic shedding of the unsteady vortex from the inlet
plane jet played a key role on the distribution of the flow pattern in the test tank. The shedding frequency of
this unsteady vortex just equaled to the frequency of the self-induced sloshing (which means it can be
coupled with the eigenvalue of the water in the test tank). So the periodical shedding of the unsteady vortex
can be suggested to be the excitation source of the resonated oscillation (self-induced sloshing).
However, where does this unsteady vortex come from? Since this unsteady vortex was originated from
the inlet plane jet, the instability of the inlet plane jet may be conjectured to be the source of this unsteady
vortex. It was well known that, according to the linear instability theory (Michalke (1965) and Ho et al.
(1984)), the most unstable mode in the plane jet should satisfy the equation:
fθ
= 0.017
St θ =
U
For the present research case, the velocity at the inlet of the test tank was about 0.333m/s, and the
momentum thickness at the inlet of the test tank was about 0.88mm according to the LDV measuremnt. So
the most unstable mode of the inlet plane jet is about 6.4Hz, which equals 4 times of the self-induced
sloshing (eigenvalue of the water in the test tank). So the instability of the inlet plane jet may be suggested
to be real excitation source of the self-induced sloshing in the test tank. When the unstable mode of the inlet
plane jet is coupled with the eigenvalue of the water in the test tank, the resonated oscillation (self-induced
sloshing) is expected to occur.
(a). U componet at point
(b). V componet at point
(X=10mm,Y=110mm, Z=25mm)
(X=90mm,Y=110mm, Z=25mm)
Figure 9. The power spectrum profiles by LDV measurement
Figure 9 shows the power spectrum of the velocity at two typical points in the test tank by LDV
measurement. From the figure, it can be seen that, besides the peak at the frequency of self-induced
sloshing (also the eigenvalue of the water in the test tank, f0=1.6Hz), the sub-peaks can also be found at the
frequencies of 2f0, 3f0 and 4f0. This means that due to the frequency toning of the water in test tank
(oscillating body), only the some modes, whose frequency can be coupled with the eigenvalue of the
oscillating body, can have advantageous growing rate. This also verified the above analysis.
Okamoto et al.(1991) had reported that the self-induced sloshing in the test tank occurred just in a
certain range of the flow rate and water level in the test tank. The "resonance model" suggested by the
present paper could also be used to explain such kind of phenomena. The flow rate changes in the test loop
may cause the change of the inlet plane jet condition, which will result in the change of the instability of the
inlet plane jet. This may cause the couple or uncouple of the unstable mode in the inlet plane jet with the
eigenvalue of the water in the test tank, so the self-induced sloshing can just be observed in a certain range
of the flow rate in the test loop. The water level change in the test tank will cause the change of the
eigenvalue of the water in the test tank, which may also result in the couple or uncouple of the unstable
mode of the inlet plane tank with the eigenvalue of the water in the test tank. So, the self-induced sloshing
was just observed in the certain range of the water level in the test tank.
CONCLUSION
The self-induced sloshing in a rectangular tank with circulating flow was investigated experimentally
by using PIV technique. The instantaneous flow field, time average value and phase average result of the
PIV measurement were used to investigate the mechanism of the self-induced sloshing. Besides the two
steady vortices in the left lower side and right side of the test tank reported by Okamoto et al. (1993a), a
new unsteady vortex was found in the test tank which was shedding periodically from the inlet plane jet.
The shedding frequency of this unsteady vortex equals to the frequency of the self-induced sloshing, which
also equals to the eigenvalue of the water in the test tank. When the water level of the free surface at the left
side of the test tank increased from its lowest position to its highest position, the unsteady vortex was found
to be generated and grown up. When the water level of the free surface at the left side of the test tank
decreased from its highest position to its lowest position, the unsteady vortex moved downstream and then
engulfed by the large steady vortex in the right side of the test tank. The flow pattern in the test tank
changed seriously with the evolution of the unsteady vortex.
Based on the above experimental result, resonated oscillation was suggested to be the mechanism of
the self-induced sloshing, and the instability of the inlet planet jet was conjectured to be the excitation
source of the self-induced sloshing.
ACKNOWLEGEMENT
The authors would like to thank the "PIV-STD" project for providing some of the experimental facility
for present research. The research fellowship provided by Japan Society for Promotion of Science (JSPS) to
the first author, and the support for the Original Industrial Technology R&D Promotion Program from the
New Energy and Industrial Technology Development Organization (NEDO) of Japan are also
acknowledged.
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