Experimental study on vortex induced vibration (VIV) of a wide-D-section cylinder in a cross flow Qingyang Wang, Mogeng Li, Shengjin Xu PII:… [628153]

Accepted Manuscript
Experimental study on vortex induced vibration (VIV) of a
wide-D-section cylinder in a cross flow
Qingyang Wang, Mogeng Li, Shengjin Xu
PII: S2095-0349(15)00008-2
DOI: http://dx.doi.org/10.1016/j.taml.2015.01.002
Reference: TAML 7
To appear in: Theoretical and Applied Mechanics Letters
Received date: 30 September 2014
Accepted date: 17 December 2014
Please cite this article as: Q. Wang, M. Li, S. Xu, Experimental study on vortex induced
vibration (VIV) of a wide-D-section cylinder in a cross flow, Theoretical and Applied
Mechanics Letters (2015), http://dx.doi.org/10.1016/j.taml.2015.01.002
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Manuscript submitted to Theoretical & Applied Mechanics Letters
1 Experimental study on vortex induced vibration
(VIV) of a wide -D-section cylinder i n a cross flow
Qingyang Wang1, Mogeng Li1 and Shengjin Xu1, a)
1) School of Aerospace Engineering, Tsinghua University, Beijing, China
a) Corresponding author. Email: [anonimizat]

Abstract Wake structures and VIV of a spring -supported wide -D-section cylinder were
experimentally investigated using an X -wire, a novel phase -locked particle image v elocimetry (PIV)
and an acceleration sensor at a low speed wind tunnel. Compared with the fixed case, the 2P (two pair)
vortex mode as defined by Gova rdhan and Williamson (2000) rather than S (single vortex) mode
exists in the wake . The velocity deficit behind the cylinder is much larger than that of fixed case . The
mean drag coefficient increases from 1.4 2 for the fixed case to 1.6 4 for the vibrating c ase. T he
Reynolds stress present s even distribution and small with increased distance of X/D= -2 to -10. The
power spectra density based on accelerator and hot wire data present s a highlight identical. It shows
that after a strong interaction the cylinder vibration and the vortex shedding come into a stable state.
The vortex shedding is totally locked on and controlled by the cylinder vibration .

Keywords wide D -section cylinder , hot wire, phase -locked PIV , vortex induced vibration , lock -on

Flow induced v ibration (FIV) of structures is frequently seen in industrial manufacture s, such as
in mechanical engineering, civil engineering, chemical engineering, marine engineering, aerospace
engineering, thermal power engineering and so on . The structures employed in those fields are
initially designed to bear load ings, contain fl ow or provide heat transfer surface without considering
fluid dynamical optimization [1]. The structures immersed in a fluid flow could be ea sily subject to
fluid force s. Especially , fluid force fluctuation may resul t in vortex induced vibration (VIV) [2], even
galloping or flutter unless the structur al collapse s occur . The VIV easily occurs or not often depends
on the shapes of structures, Reynolds number, scenario of facing flow , etc. Whe ther to suppress or to
utilize the VIV , or to guarantee the structure s safe, or to realize flow control, it is both essential and
crucial to investigate details on the interaction between the VIV structure and the fluid flow. It
motivates the present study .
There are innumerable experimental and theoretical studies on VIV of structures with simple
cross section shapes . The circular cylinder is the simplest geometry and most commonly used in the
industry [3]. Numerous experimental studies show that vortex shedding behind the circular cylinder
cause s fluctuation lift resulting in a periodical vibration , which is so-called VIV . So far , the VIV of
other bluff bodies has also attracted people ’s interest [4, 5]. The key of VIV problem exists in a strong
interactio n between the cylinder motion and vortex shedding [6, 7]. The VIV of a cylinder is often
subject to the effects of cross section shape of the cylinder, Reynolds number, Strouhal number , added
mass effect , structural stiffness of the cylinder and damping ratio [8, 9]. Many semi -empirical models
have been built to predict the dynamics of the VIV cylinder . Meanwhile, the two most popular models
are the harmonic model and the wake oscillator model , respectively [1, 10, 11 ]. With the two models
one may give a simple predict ion to the VIV of a cylinder in the cross flow.

2
2 In this paper, we aim to study the flow structure and oscillati on of a wide -D-section cylinder
since the study is significant to engineering application s but being less concerned . [12] The flow
structures around the c ylinder are studied using a novel phase -locked Particle Image Velocimetry
(PIV). The vibration of cylinder is monitored by an acceleration sensor . The velocity profile s and
Reynolds stress behind the cylinder are measur ed by an X-wire.

The experiment was carried out at a low speed wind tunnel with a square test section (0.5 m×0.5
m) of 2m long. The wind speed can be adjusted from 0 m/s to 40 m/s. Turbulence intensity was less
than 0.5% in the free stream in this experiment. A wide -D-section cylinder was horizontally
supported by two springs at each end of the cylinder. The cylinder was mounted in the middle of the
working section . The flat surface of the cyl inder was faced to the free flow and the x-y coordinate is
shown as Fig.1 . The cross section of the cylinder is show n in Fig. 1 (b). The blockage was about 5.5%.
The mass ratio m* was approximately 962, the structural damping ratio ζwas estimated to be 0.000 7
and the natural frequency fn of the spring -cylinder was 6.866 Hz. Both the na tural fre quency and the
damping ratio were measured in the still air. The free strea m velocity U0 in this experiment was fixed
at 4.0 m/s. The corresponding Reynolds number defined by the speed of free flow and the height of
the cylinder was about 8000 .
Test sectionHot wireLaser sheet Flow
x
y
+
–
Wind tunnel+
-Double
pulsed
YAG
laserPIV
control
system
Camera
control device
CCD
cameraSpringAmplifierdSPACE
control
systemMATLAB/
Simulink
Acceleration
sensor

(a) (b)
Fig.1 Experimental setup and dimension s of the wide -D section cylinder
The flow structures behind the wide -D-section cylinder were captured by a standa rd LaVision
Particle Image Velocimetry (PIV) system . The smoke particle (around 2
μm in diameter) generated by
paraffin oil was used as trace particle . The double pulsed YAG Laser sources of a wavelength of
532nm serve d as flow illum ination devices in the test zone . The maximum energy output of the laser
is about 120mJ. The thickness of the laser sheet was about 1mm. A single CCD camera with a
resolution of 2048pixels
2048 pixels for each image was used to capture the flow structure. The
cylinder surface and the wind tunnel wall illuminate d by the laser sheet were painted black to
minimize the light reflection noise . The green light generated by the laser source is allowed to pass
through and goes inside CCD camera by an optical filte r, of which the passing wavelength is 532nm .
Velocity vector fields were calculated from the raw images by a cross -correlation algorithm built in
the Davis softw are of the LaVision system. The interrogation area was 32pixels☓32pixels and the
overlap was 50%. The weak correlation vectors were automatically removed in the Post-processing .
To measure the flow structures at the designated vibration phase of the sprin g-supported cylinder, the
PIV was trigger ed by a dSPACE real -time control desk combine d with the MATLAB/Simulink
platform . Thus, a series of flow structure according with the designated vibration phase could be
measured by this modified PIV technique . After phase -average calculation, a smooth and average d
D=0.03m
h=0.045mflow

Manuscript submitted to Theoretical & Applied Mechanics Letters
3 flow velocity field can be obtained for arbitrary vibration phase of the cylinder.
The vibration o f the wide -D-section cylinder was measur ed by a miniature B&K acceleration
sensor (Delta 4 516) fixed at one end of the cylinder . The signal after amplifier was collected by a NI
6521 acquisition system at a sampling frequency
5kHzsamplef
, and the sampling time was about 30s.
The velocity profile behin d the wide -D-section cylinder was measured by an IFA 300 constant
temperature hotwire anemometer with an X-arrangement hot film sensor Model 1246 -20W (50.8
m
of diameter) at X/D = -2, X/D = -5 and X/D = -10, respectively. Sixty -one points were measured along
y direction at the range of Y/D = -3 to 3. Signals was offset, amplified, digitized using a n 8 channel
A/D board and then recorded by a computer at a sampling frequency
5kHzsamplef
. The sampling
time was about 26s. The vortex shedding frequencies of the cylinder were calculated based on the
power spectral density of hot wire measurements.

Instantaneous vorticity field of the fixed wide -D-section cylinder is show n in Fig.2 . V ortices
alternatively shed from the leading corner of the cylinder . It distinguish es from that of fixed circular
cylinder [13] and square cylinder [14]. The vort ices stretch much longer in the wake of the D -section
cylinder than that of the circular or square cylinder. The vorticity is not available below the cylinder
where the flow is in the shadow.
(c) 3T/4 (d) T2.74
-2.843.52
2.45
-2.503.23
-1.813.56 3.90
2.80
-2.80
(a) T/4
(b) T/2

Fig.2 Normalized vorticity contour s (
*
0/zDU
) for the fixed wide -D cylinder , Re=8000

Figure 3 shows that the phase average results for normalized vorticity contours at designated
vibration phase for the vibrating case. Each picture is the average of 300 pairs of vorticity contour
which obtained using phase -locked PIV at a designated vibration phase. Figure 3( 1) shows the details
in vibration phases (45 degree of phase interval) according with the vorticity contours in Figure 3( 2).
Unlike the fixed case of the wide -D cylinder, th e vortices form two pair vortex structure in the wake
which was so-called 2P mode according to Govardhan and Williamson (2000) . Figure 3(2a) – (2d)
show the cylinder is moving down to the outmost position and coming back to the balance point (Fig.
3(2d)). Figure 3(2d) –(2h) show vortici ty change at the range of another 180 phase angle. A
vortex -pair including two vortices with opposite sign voticity present s at each side of the cylinder.
One of vortex in the pair forms from the natural shedding at the corner of the cylinder, another is from
the induced flow because of the cylinder motion. Two vortex -pairs alternatively occur at each side of
the cylinder.

4
4
(a) 45°phase (b) 90°phase-3.233.50 2.58
3.20
-2.10
(f) 270°phase2.80
-2.96(d) 180°phase
(g) 315°phase (h) 360°phase-1.70 2.30
-5.903.40
-4.601.72
6.40
-2.102.104.50
-3.50(e) 225°phase3.40
-2.701.17(c) 135°phase
(a) 45°phase (b) 90°phase-3.233.50 2.58
3.20
-2.10
(f) 270°phase2.80
-2.96(d) 180°phase
(g) 315°phase (h) 360°phase-1.70 2.30
-5.903.40
-4.601.72
6.40
-2.102.104.50
-3.50(e) 225°phase3.40
-2.701.17(c) 135°phase
(a)
(b)(c)(d)(e)(f)
(g)
ty
(h)
(1) Phase for each picture
(2) Normalized vorticity

Fig.3 The normalized vorticity
*
0/zDU
for Re=8000

The mean velocity deficit at X/D= -2, X/D=-5 and X/D= -10 obtai ned by an X-arrangement hot
film is illustrated in Fig .4. The area of the deficit becomes larger as increased X/D since the wake is
still developing in this range of X/D. The deficit area of vibrating case is larger than that of the fixed
case. The vibrat ing cylinder broadened the velocity deficit in transverse direction, compared to the
fixed cylinder case.

(a) X/D = -2 (b) X/D = -5 (c) X/D = -10
Fig.4 The mean velocity deficit at X/D= -2, X/D= -5 and X/D= -10

Manuscript submitted to Theoretical & Applied Mechanics Letters
5

(a) X/D = -2 (b) X/D = -5 (c) X/D = -10
Fig.5
2
0/u u U
profile along y direction at X/D= -2, X/D= -5 and X/D= -10

(a) X/D= -2 (b) X/D= -5 (c) X/D= -10
Fig.6
2
0/v v U
profile along y direction at X/D= -2, X/D= -5 and X/D= -10

(a) X/D= -2 (b) X/D= -5 ( c) X/D= -10
Fig.7
2
0/u v U
profile along y direction at X/D= -2, X/D= -5 and X/D= -10

To estimate the mean dra g, the algorithm [16-18] taking the Reynolds normal stress into account is
adopted as Eq. (2.1).
122
20 0 0
02 1 21
2yy
D
d
yy
IIF U U y v v u u yC d dU U D U DUD
(2.1)
where
is the density of the fluid,
0U is the free stream velocity,
DF is the drag force.
Eq. (2.1) includes two component s, namely the momentum integral I1 and I2, with contrib ution
from mean velocity and Reynolds normal stress, respectively.
Fig.5 & Fig.6 give
2
0/u u U
and
2
0/v v U
profile along y direction at X/D = -2, X/D = -5 and X/D
= -10, respectively.
2
0/u u U
and
2
0/v v U
decrease with increased
X/D
for both fixed and
vibrating case. At X/D = -10, both
2
0/u u U
and
2
0/v v U
decrease to one -third of the value at X/D =

6
6 -2. It indicates the I2 will have less effect as inc reased X/D. This res ult is in agreement with Antonia’s
study [16].Fig.7 shows the term regarding the Reynolds shear stress
2
0/u v U
varies along the y
direction. Similarly,
2
0/u v U
becomes very smaller and even along y d irection at X/D = -10 than that
of at X/D = -2 and -5. Furthermore,
2
0/u v U
for vibration case is always smaller than that of fixed
case for each X/D. Consider the distribution of
2
0/u v U
for the vibrating wide -D cylind er, one may
use this to control the turbulent mixing issues. Table 1 lists the calculated I1, I2 and drag coefficient
according to Eq. (2.1) at different X/D. To minimize the measurement error, the mean drag for three
X/Ds is given. The Cd mean of the fixe d wide -D cylinder is about 1.42, which is slightly larger than
that of a circular cylinder (table 2). For the vibrating wide -D cylinder, the Cd mean increases to 1.64
but is lower than that of a square cylinder (see table 2).

Table 1 Cd of the wide -D-section cylinder

Fixed wide -D-section cylinder Vibrating wide -D-section cylinder
(Re=8000 )
I1 I2 Cd I1 I2 Cd
X/D=-2 1.1408 0.2421 1.3829 1.6010 0.0306 1.6316
X/D=-5 1.0518 0.3688 1.4207 1.4670 0.2000 1.6671
X/D= -10 1.3943 0.0499 1.4442 1.5721 0.0547 1.626 8
Mean value 1.1956 0.2202 1.4159 1.5467 0.0951 1.6418

Table 2 Cd for different cylinders
Fixed wide -D-section
cylinder Vibrating
wide -D-section cylinder Fixed circular section
cylinder [19] Fixed square section
cylinder [20]
1.4159 1.6418 1.2 2.0

To measure the structural frequency of the spring -supported wide -D cylinder, acceleration of the
cylinder is obtained when it is in a damped free vibration. The vibration is approximately linear.
According to the measurement as shown as Figure 8, the s tructural damping ratio ζis estimated to be
0.000 7 and the structural natural frequency fn is 6.866 Hz, or 0.0515 normalized by D and free stream
velocity U 0. As the steady VIV of the wide -D cylinder occurs, the acceleration becomes apparently to
be periodical . The vibration frequ ency is identical to the natural frequency all the time . Even if the
flutter occurs, the vibration amp litude increases rapidly to a new value but the vibration frequency
still remains identical to the natural frequency . That is because the vortex shedding frequency is
locked on the cylinder vibration. At the beginning of the cylinder vibration, the cylinder is forced to
vibrate by the periodical force caused by vortex shedding. Hence, the vibration frequency is slightly
higher than that of structural natura l frequency of the cylinder, say 0.0878 to 0.0956 norma lized
frequency as shown as the hot wire measurement in Figure 10 (not shown in acceleration data) . Power
spectra density functions for different X/D from hot wire measurement are presented in Fig.10&1 1.

Manuscript submitted to Theoretical & Applied Mechanics Letters
7 The fixed case is in Fig.10 and the vibrating case is in Fig.11. For the fixed case, the vortex shedding
frequency at X/D = -2 (0.0956) is slightly higher than that at X/D = -5 (0.0878) and -10 (0.0876) . It
shows that the convective velocity of the vort ex is a little bit rapid that is probably caused by blockage
effect near the cylinder. The convective velocity keeps nearly constant speed downstream . For the
vibrating case, the vortex shedding is locked on the natural frequency of the cylinder. The domin ant
peak of the normalized frequency occurs at 0.0515. Meanwhile, double and triple frequency of the
value of 0.0515 also can be found in the power spectra density function. Those peaks indicate that the
vortex is breaking into many small vortices downstre am.

5 6 7 8 9 10-0.200.2
t(s)a(m/s2)
10-310-210-1100101-150-100-500
fD/U0Ea0.0515

Fig.8 Acceleration and its power spectra density function for damped free vibration of the cylinder

5 6 7 8 9 10-40-2002040
t(s)a(m/s2)
10-310-210-1100101-150-100-50050
fD/U0Ea0.0515

Fig.9 Acceleration and its power spectra density function for steady VIV of the cylinder

8
8
10-210-1100
fD/U0Eu
10-210-1100
fD/U0Eu
10-210-1100
fD/U0Eu
10-210-1100
fD/U0EuY/D=0Y/D=1Y/D=2Y/D=30.0956
10-210-1100
fD/U0Eu
10-210-1100
fD/U0Eu
10-210-1100
fD/U0Eu
10-210-1100
fD/U0Eu
Y/D=0Y/D=1Y/D=2Y/D=30.0878
10-210-1100
fD/U0Eu
10-210-1100
fD/U0Eu
10-210-1100
fD/U0Eu
10-210-1100
fD/U0Eu
Y/D=0Y/D=1Y/D=2Y/D=30.0876(a)X/D=-2
(b)X/D=-5
(c)X/D=-10

Fig.10 P ower spectra density from hot wire signal for the fixed case. (a) X/D = -2; (b) X/D = -5; (c)
X/D = -10

Manuscript submitted to Theoretical & Applied Mechanics Letters
9
10-210-1100
fD/U0Eu
10-210-1100
fD/U0Eu
10-210-1100
fD/U0Eu
10-210-1100
fD/U0EuY/D=0Y/D=1Y/D=2Y/D=30.1027
0.1542 0.0515
10-210-1100
fD/U0Eu
10-210-1100
fD/U0Eu
10-210-1100
fD/U0Eu
10-210-1100
fD/U0Eu
Y/D=0Y/D=1Y/D=2Y/D=30.1027
0.1542 0.0515(a)X/D=-2
(b)X/D=-5
10-210-1100
fD/U0Eu
10-210-1100
fD/U0Eu
10-210-1100
fD/U0Eu
10-210-1100
fD/U0Eu
Y/D=0Y/D=1Y/D=2Y/D=30.1027
0.1542 0.0515(c)X/D=-10
Fig.1 1 Power spectra density from hot wire signal for the vibrating case. (a) X/D = -2; (b) X/D = -5; (c)
X/D = -10
The near wake s of a spring supported wide D -section cylinder both for fixed and vibrating case
have been studied using PIV, X-wire and an acceleration sensor. The following conclusions can be
drawn .
The flow structure is influenced by the vibration of the cylinder . The wake of the vibrating
cylinder presents two pair vortex structure (2P), which is different from 2S mode contained in the
fixed case. The cylinder vibration results in a larger drag than that of the fixed case. In the steady VIV ,
the vibration frequency is identical to the structural natural frequency even if the flutter occurs.

This work wa s supported by the National Natural Science Foundation of China ( 11472158 ).

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