Download experimental study on the flow field between two square cylinders in

The Seventh Asia-Pacific Conference on
Wind Engineering, November 8-12, 2009,
Taipei, Taiwan
EXPERIMENTAL STUDY ON THE FLOW FIELD BETWEEN TWO
SQUARE CYLINDERS IN TANDEM ARRANGEMENT
Hiroshi Hasebe1, Kenji Watanabe2, Yuki Watanabe2 and Takashi Nomura3
Research Associate, Department of Civil Engineering, CST, Nihon University
Kanda-Surugadai 1-8-14, Chiyoda-ku, Tokyo, 101-8308 Japan
[email protected]
2
Undergraduate student, Department of Civil Engineering, CST, Nihon University
Kanda-Surugadai 1-8-14, Chiyoda-ku, Tokyo, 101-8308 Japan
3
Professor, Department of Civil Engineering, CST, Nihon University
Kanda-Surugadai 1-8-14, Chiyoda-ku, Tokyo, 101-8308 Japan
[email protected]
1
ABSTRACT
Flow field between two square cylinders in tandem arrangement is investigated. The surface pressure
distributions vary considerably between the spacing ratio L/D = 3 and L/D = 4. The velocity between two square
cylinders of L/D = 4 is measured by means of a split-fiber probe. The phase-averaging technique is applied to
the measured velocity data with reference to the surface pressure of the upstream cylinder. According to the
phase-averaged velocity, the flow between two cylinders shows two patterns. One is diagonal flow which
intersects diagonally between two cylinders. The other is high curvature flow which varies the flow direction
from upward (downward) to downward (upward) between two cylinders. These two flow patterns vary
periodically. The Reynolds stress evaluated from the periodical component of the velocity occupies about 80%
of the Reynolds stress evaluated from the total fluctuating component of the velocity. Therefore the periodical
component of the velocity which is caused by the vortex shedding from the upstream cylinder has a great
influence on the property of the turbulent flow structure between two square cylinders.
KEYWORDS: SQUARE CYLINDER, TANDEM ARRANGEMENT, SPLIT-FIBER PROBE,
PHASE AVERAGE
Introduction
There are various tandem-arranged structures or structural components which are
exposed in wind, for example, the parallel cables of cable-stayed bridges, the twin hanger
ropes and the tower of suspension bridges. It is well known that serious vibrations called as
“wake galloping” or “wake induced flutter” occur in the parallel cables and twin hanger ropes.
Therefore, aerodynamic characteristics of tandem-arranged structures have been studied
widely [Shiraishi et al. (1986) and Tokoro et al. (2000)]. However, since it is difficult to
measure, only limited information is available on characteristics of the flow field between
tandem-arranged structures [Obi et al. (2006)].
In the present study, the flow field between two square cylinders in tandem
arrangement is investigated. The surface pressure distributions are measured for four cases of
the spacing ratio. The velocity between the two cylinders is measured by means of the splitfiber probe. The phase-averaging technique is applied to the measured velocity data in order
to realize flow pattern. In addition, the Reynolds stress between two square cylinders is
investigated.
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
800mm
D
9mm 6mm@7 9mm
pressure taps
U∞
SFP
B
C
F
G
E
H
y
400mm
A
wind
6mm
x
D
8mm@3
D
z
5D
L
measurement
plane
y
L
x
Figure 1: Arrangement of two square
cylinders
Figure 2: Location of pressure taps
Experimental setup
The experiment is conducted in an open circuit wind tunnel. The test section has a
400mm×400mm square cross section and 800mm long. The turbulent intensity of the free
stream velocity is about 1.5%. The test bodies adopted in the present study are two square
cylinders with a width D of 60mm, an axial length S of 356mm and two end plates on both
sides. As shown in Fig.1, the upstream square cylinder is placed at 5D distance from the
entrance of the test section. The downstream square cylinder is located in the streamwise
direction. The space between two square cylinders is designated by L.
In order to measure the surface pressure, each single square cylinder has 16 pressure
taps of 1.3mm diameter at the center of the span. According to [Sakamoto et al. (1987)], 8 or
10 pressure taps are necessary on a single side of the square cylinder. Therefore, 8 pressure
taps are allocated on the upper surface of each square cylinder as shown in Fig.2. Considering
the symmetry, 4 pressure taps are allocated on the front and rear surface. These pressure taps
are connected to a differential pressure transducer (TOA Industry, MP-32). Since the width of
test bodies is determined to allocate the sufficient number of pressure taps, the blockage of the
present study is 15%, consequently.
The velocity measurement between two square cylinders is conducted by means of a
split-fiber probe (DANTEC, 55R55). The measuring points are aligned on a plane normal to
the cylinder axis. The measurement plane is located at middle of the cylinder span as shown
in Fig.1. The pressure and velocity signals are digitized for 30s at the rate of 500Hz. The
averaging time for the time-average of the measured data is 30s. For the pressure
measurement, the free stream velocity is set to 12.0m/s (Re = 50,000). On the other hands, for
the velocity measurement, the free stream velocity is decreased to 6.0m/s (Re = 25,000) since
the output voltage from a split-fiber probe exceeds the range which can be measured.
Surface pressure distribution corresponding to the spacing ratio
The surface pressure measurement is conducted at four cases of the spacing ratios
(L/D = 2, 3, 4 and 5). Figures 3 and 4 show the distributions of time-averaged surface pressure
j , respectively. The surface pressure
coefficient CP and fluctuating pressure coefficient C
P
distributions of L/D = 4 and 5 differ considerably from those of L/D = 2 and 3; with regard to
the time-averaged pressure, the downstream cylinder reveals completely different
distributions; the fluctuating pressures of L/D = 4 and 5 are magnified considerably.
For L/D = 2 and 3, on the upper surface of the downstream square cylinder (surface FG), the recover of the pressure like reattachment-type rectangular cylinder are observed. For
L/D = 4 and 5, on the front surface of the downstream square cylinder (surface E-F), timeaveraged pressure coefficients becomes approximately zero. As shown in Fig.5, for L/D = 2,
only the negative pressure is measured at the center of the front surface of the downstream sq-
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
2
2
1.5
L/D=2
L/D=3
L/D=4
L/D=5
1
0.5
CP
L/D=2
L/D=3
L/D=4
L/D=5
1.5
j
C
P
0
1
-0.5
-1
0.5
-1.5
-2
A
B
C
D
E
F
G
H
Position
Figure 3: Distributions of
the time-mean pressure coefficient
0
A
B
C
D
E
F
G
H
Position
Figure 4: Distributions of
the fluctuating pressure coefficient
uare cylinder (point E). On the contrary, for
L/D = 4, the surface pressure at point E
200
L/D = 4
fluctuates between positive and negative
values. As a result, time-averaged pressure
100
becomes approximately zero. From the
0
observation of the pressure fluctuation, it is
inferred that the vortex emanated from the
-100
upstream square cylinder impinges to the
L/D = 2
-200
front surface of the downstream square
cylinder.
-300
29.5
29.6
29.7
29.8
29.9
30
Considerable change of the distritime (s)
bution of the surface pressure between L/D =
Figure 5: Time history of the surface
3 and 4 is in accordance with the experimentpressures at point E in Fig.2
tal work by [Sakamoto et al. (1987)]. [Liu et
al. (2002)] show that the flow pattern changes
between L/D = 3 and 4 by the flow visualization. However, the Reynolds number of their
experimental work is 2,700 which is smaller than that of the present study (Re = 25,000). In
addition, they did not measure the velocity between the two square cylinders in detail. In the
present study, for the purpose of the detailed investigation of the flow field between the two
square cylinders, the velocity is measured at densely distributed locations between the two
square cylinders.
pressure (Pa)
300
Treatment of outputs from a split-fiber probe
Since the distributions of the surface pressure suggest the existence of the fluctuating
flow between the two square cylinders in case of L/D = 4 and 5, the measurement of the
velocity between the two square cylinders with the spacing ratio L/D = 4 is conducted by
means of a split-fiber probe. The locations of 72 measurement points are shown in Fig. 6. At
each point, the velocity components with respect to the x-axis (U) and the y-axis (V) are
measured. In order to measure the velocity near the square cylinders, a split-fiber probe is set
in the plane as parallel to the axis of the cylinder (z direction) as shown in Fig.1. For the
measurement of the velocity component V, the split-fiber probe is set as orthogonal to the yaxis as shown in Fig.7. For the measurement of the velocity component U, the split-fiber
probe is rotated 90° around z-axis.
The sensor of the split-fiber probe is wrapped around a quartz core, and then, the filmlike sensor is split into two sensors as shown in Fig.7. Therefore the split-fiber probe provides
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
Reference pressure point
(Point R)
Measurement point
30mm
Point P
6mm
y
wind
V2
split
x
8mm@6
z
CH II
y
CH I
6mm
x
V1
20mm
20mm@7
20mm
Figure 7: Head of
a split-fiber probe
Figure 6: Location of the velocity measurement points
velocity (m/s)
velocity (m/s)
CH I
CH II
8
6
4
2
0
29.5
29.6
29.7
29.8
29.9
30
8
6
4
2
0
-2
-4
-6
-8
29.5
time (s)
29.6
29.7
29.8
29.9
30
time (s)
Figure 9: Combined velocity data
Figure 8: Measured data at point P
by a split-fiber probe
two output signals. For example, when the flow comes from V1 direction indicated in Fig.7,
the output of channel I sensor becomes larger than that of channel II sensor. Figure 8 shows
outputs from the two sensors of a split-fiber probe when the velocity component V is
measured at point P indicated in Fig.6. Since it is inferred that the periodical vortex shedding
occurs, outputs from two sensors increase alternately. These two signals should be combined
into one velocity signal. The result in Fig.8 shows that when the output from one sensor
becomes large, the output from the other sensor becomes almost zero. Moreover, the rounded
two sensors of the split-fiber probe are facing to the opposite directions. Therefore, in the
present study, the following relation is employed to combine the two signals:
⎧⎪ V1
V =⎨
⎪⎩−V2
(V
(V
1
≥ V2
1
< V2
)
)
(1)
where V1 and V2 are the velocity components measured by the two sensors, respectively.
Phase averaging technique
According to [Hussain et al. (1970)], the instantaneous velocity ui is decomposed into
the following three components:
ui = U i + uci + ur′ i = ui + ur′ i
(2)
where U i is the time-mean component, uc i is the periodical component ‘with zero mean’ and
ur′ i is the random component. ui = U i + uc i is the phase-averaged component. Since uc i and
(
)
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
measured
filterd
sampled
4
Fourier spectrum (m/s)
8
velocity (m/s)
6
4
2
0
-2
-4
-6
-8
29.5
3.5
3
2.5
2
1.5
1
0.5
0
29.6
29.7
29.8
29.9
0
30
50
100
time (s)
200
250
frequency (Hz)
(a): Time history of the velocity
at point P in Fig.6
(b): Fourier spectrum of the measured
velocity at point P in Fig.6
measured
filterd
sampled
0
150
20
Fourier spectrum (Pa)
pressure (Pa)
-20
-40
-60
-80
-100
-120
-140
29.5
15
10
5
0
29.6
29.7
29.8
29.9
30
time (s)
(c): Time history of the surface pressure
at point R in Fig.6
0
50
100
150
200
250
frequency (Hz)
(d): Fourier spectrum of the measured
surface pressure at point R in Fig.6
Figure 10: Process of the phase average
ur′ i are zero mean components, the time averaging technique to measured velocity data can
not reveal the pattern of the fluctuating flow between two square cylinders. Therefore, in
order to obtain the phase-averaged velocity ui , the phase averaging technique [Lyn et al.
(1994) and Perrin et al. (2007)] is applied to the present measured velocity data.
The phase averaging technique needs the referential signal to define the flow phase. In
the present study, the surface pressure of the upstream cylinder, of which the location is
shown in Fig.6, is used as the reference signal. The process to compute the phase-averaged
velocity consists of the following three procedures:
1) Simultaneous measurement of velocity and pressure
The velocity and the surface pressure are measured simultaneously. Typical result of
measured data, velocity component V which is measured at point P indicated in Fig.6, surface
pressure which is measured at the point R in Fig.6 and their Fourier spectrums are shown in
Figs.10 (a)-(d). To remove the random component ur′ i from the measured data, the data is
filtered by a low-pass filter. As shown in Figs.10 (b) and (d), Fourier spectrums of the
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
measured velocity and the surface pressure have same peak-frequency at 12.8Hz ( St = 0.128 )
which is in accordance with the Strouhal number of the single square cylinder [Lyn et al.
(1995)]. Therefore, the cut-off frequency of the low-pass filer is set at 30Hz which is twice
high frequency of the vortex shedding from the upstream cylinder.
2) Subdivision of the measured data
To define the phase, the measured data is divided into a series of single cycle periods.
The period is defined as the interval between peaks of the pressure signal which are shown in
Fig.10(c) by circle symbols.
3) Extraction of data at same phase
From every divided data, velocities at the same phase are extracted and averaged. In
the present study, each period is divided into 20 phases. As a result, the phase-averaged
velocity ui is obtained. In Fig.10(a), circle symbols indicate the extracted velocity data at
phase φ = 0 .
Phase-averaged velocity between two square cylinders in tandem arrangement
The distributions of the phase-averaged velocity vectors and the streamlines are shown
in Fig.11(a)-(h). At phases φ = 0 φ = φ 2π and φ = 10 20 , large vortices as large as the square
cylinder are observed behind the upstream cylinder indicated as “A” in Fig.11(a) and as “B”
in Fig.11(e) respectively. The advective speed of the vortex is about 2.6m/s calculated from
the location of the vortex center at every phase. It is about 40% of the inflow velocity
(6.0m/s). At phases φ = 3 20 and 5 20 , since the vortex “B” emanated from the lower side of
the upstream cylinder has passed the region between two cylinders, the upward flow is
formed almost of all the region between two cylinders. At phases φ = 8 20 and 10 20 , rolling
(
)
A
B
A
B
(a) : φ = 0
(e) : φ = 10 20
A
B
(b) : φ = 3 20
(f) : φ = 13 20
A
B
(c) : φ = 5 20
(g) : φ = 15 20
A
B
(d) : φ = 8 20
(h) : φ = 18 20
Figure 11: Phase-averaged velocity vector and streamline
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
0.35
0.45
0.10
0.05
0.10
0.25
0.15
(a) u ′ U
2
(b) v′2 U in2
2
in
Figure 12: Distribution of normal components of the Reynolds stress
0.30
0.35
0.05
0.05
0.20
0.10
(a) u U
2
c
2
in
(b) vc2 U in2
Figure 13: Distribution of normal components of the Reynolds stress evaluated
from the periodical component of the velocity
up from the upper side of the upstream cylinder forms the downward flow behind the
upstream cylinder. On the other hands, the vortex “A” emanated from the lower side of the
upstream cylinder forms the upward flow in front of the downstream cylinder. Therefore, high
curvature of the streamline exists between two cylinders at these phases. As shown in
Figs.11(e)-(h), at phases from φ = 10 20 to 18 20 , the flow patterns are symmetric to the flow
at phases from φ = 0 to 8 20 with respect to the vertical axis through both centers of the two
cylinders.
Distribution of the Reynolds stress
Since the fluctuating component of the velocity ui′ is calculated as ui′ = ui − U i , where
ui is the instantaneous velocity, U i is the time-averaged component, the Reynolds stress ui′u ′j
can be investigated. The fluctuating component of the velocity ui′ is further decomposed to
the periodical component uc i and the random component ur′ i as ui′ = uc i + ur′ i . Therefore, the
Reynolds stress calculated from the periodical component uc i and the Reynolds stress
calculated from the random component ur′ i can be evaluated. In this chapter, we discuss that
how these components contribute to the total Reynolds stress ui′u ′j .
Figures 12(a) and (b) show contours of the Reynolds stress ui′u ′j . Since the
simultaneous measurement of the velocity components U and V is not conducted, only the
normal components of the Reynolds stress u ′2 and v′2 are investigated. u ′2 and v′2 are nondimensionalized by square of the inflow velocity Uin (=6.0m/s). As shown in Fig.12(a), the
distribution of u ′2 component has two peaks near the trailing edges of the upstream cylinder.
On the other hands, the distribution of v′2 component has one peak behind the upstream
cylinder. The location of the peak of the v′2 component is further from the upstream cylinder
than that of the u′2 component.
Since the periodical component of the velocity uc i is evaluated as uc i = ui − U i , the
Reynolds stress calculated from the periodical component uc i uc j can be evaluated. Figs.13(a)
and (b) show the normal components of the Reynolds stress calculated by the periodical
component of the velocity uc2 and vc2 . In comparison with Figs.12(a), (b) and Figs.13(a), (b),
The Seventh Asia-Pacific Conference on Wind Engineering, November 8-12, 2009, Taipei, Taiwan
distributions of uc2 and vc2 are quite similar to those of u′2 and v′2 . Their peaks appear at the
same locations. The peak values uc2 and vc2 occupy about 80% to that of u ′2 and v′2 ,
respectively. Therefore, the periodical component of the velocity which is occurred by the
vortex shedding from the upstream cylinder has a great influence on the property of the
turbulent flow structure between two square cylinders.
Conclusion
In the present study, for the purpose of the investigation of the flow field between two
square cylinders in tandem arrangement, the measurement of the surface pressure and the
measurement of the velocity between two square cylinders are conducted. As a result, the
surface pressure distributions vary considerably between the spacing ratio L/D = 3 and L/D =
4 in accordance with the experimental work by [Sakamoto et al. (1987)].
For L/D = 4, according to the phase-averaged velocity, the flow field between two
cylinders shows two patterns. One is the diagonal flow which intersects between two
cylinders. The other is high curvature flow which forms the upward (downward) flow behind
the upstream cylinder and the downward (upward) flow in front of the downstream cylinder.
For L/D = 4, these flow patterns vary periodically between two square cylinders in tandem
arrangement.
Between two square cylinders, the Reynolds stress evaluated from the periodical
component of the velocity occupies about 80% to the total Reynolds stress which is evaluated
from the fluctuating component. Therefore, the periodical component of the velocity has a
great influence on the property of the turbulent flow structure between two square cylinders.
Reference
Hussain, A. K. M. F. and Reynolds, W. (1970), “The mechanics of an organized wave in turbulent shear flow”,
Journal of Fluid Mechanics, 41, 241-258
Liu, C. H. and Chen, J. M. (2002), “Observations of hysteresis in flow around two square cylinders in a tandem
arrangement”, Journal of Wind Engineering and Industrial Aerodynamics, 90, 1019-1050
Lyn, D. A. and Rodi, W. (1994), “The flapping shear layer formed by flow separation from the forward corner of
a square cylinder”, Journal of Fluid Mechanics, 267, 353-376
Lyn, D. A., Einav, S., Rodi, W. and Park, J.-H. (1995), “A laser-Doppler velocimetry study of ensembleaveraged characteristics of the turbulent near wake of a square cylinder”, Journal of Fluid Mechanics, 304,
285-319
Obi, S. and Tokai, N. (2006), “The pressure-velocity correlation in oscillatory turbulent flow between a pair of
bluff bodies”, International Journal of Heat and Fluid Flow, 27, 768-776
Perrin, R., Cid, S., Cazin, S., Sevrain, A., Braza, M., Moradei, F. and Harran, G. (2007), “Phase-averaged
measurements of the turbulence properties in the near wake of a circular cylinder at high Reynolds number by
2C-PIV and 3C-PIV”, Experiments in Fluids, 42, 93-109
Sakamoto, H., Haniu, H. and Obata, Y. (1987), “Fluctuating force acting on two square prisms in a tandem
arrangement”, Journal of Wind Engineering and Industrial Aerodynamics, 26, 85-103
Shiraishi, N., Matsumoto, M. and Shirato, H. (1986), “On aerodynamic instabilities of tandem structures”,
Journal of Wind Engineering and Industrial Aerodynamics, 23, 437-447
Tokoro, S., Komatsu, H., Nakasu, M., Mizuguchi, K. and Kasuga, A. (2000), “A study on wake-galloping
employing full aeroelastic twin cable model”, Journal of Wind Engineering and Industrial Aerodynamics, 88,
247-261