OMAE2013-10454: Experimental Study on Flow Around Circular Cylinders with Low Aspect Ratio

Nantes| France | June | 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering 1
EXPERIMENTAL STUDY ON FLOW AROUND CIRCULAR
CYLINDERS WITH LOW ASPECT RATIO
June | 2013
Rodolfo T. Gonçalves
Guilherme F. Rosetti
Guilherme R. Franzini
André L. C. Fujarra
TPN – Numerical Offshore Tank
Department of Naval Architecture and Ocean
Engineering
Escola Politécnica – University of São Paulo
São Paulo, SP, Brazil

Outline
• Introduction
• Objectives
• Experimental Setup
• Results
– Force measurements
– PIV
• Conclusions

Introduction
• The flow field around
stationary low aspect
ratio cylinders, 𝐿/𝐷 < 6,
is much less understood
than the classical case of
infinite length cylinder;
• VIM in the offshore
scenario:
– Spars (1.5 < L/D < 6);
– Monocolumns (0.2 < L/D <
0.5);
– SS columns (0.4 < L/D < 3).
Models of the flow around low aspect ratio
circular cylinder. Source: Kawamura et al.
(1984)

Objectives
• Understand the aspect
ratio influence in the
forces around the
cylinder (streamwise, x,
and transverse, y,
directions) and vortex
shedding frequency:
through force
measurements.
• Visualize the flow
around the free end
and immediately behind
the cylinder where the
flow recirculates: using
PIV technique.
• Very low aspect ratio
cylinders:
0.1 ≤ 𝐿 𝐷 ≤ 2

Experimental Setup
• All the experiments were carried out in a
recirculating water channel at the NDF – Fluid &
Dynamics Research Group Laboratory facility of
USP – University of São Paulo, Brazil.
• The dimension of the test section is
7500x700x700mm and the flow has low levels of
turbulence (less than 2%).
• The model was made of PVC - polyvinyl chloride
with external diameter 𝐷=125mm and was
placed at the centerline of the channel.

Experimental Setup
Force Measurements
• A 6-DOF load cell was used to acquire the
hydrodynamic forces.
• Eight different aspect ratios were tested,
namely 𝐿/𝐷 = 0.1, 0.2, 0.3, 0.5, 0.75, 1.0,
1.5 and 2.0;
• The range of Reynolds number covers
10,000 < Re < 50,000;
• 40 different velocities to each aspect ratio;
• The changes in the aspect ratio were
made changing the water level, 𝐻, of the
water channel.
z
x
L
U
h
H Free end
Free surface
D
y
x
W
Water channel bottom
U
Water channel lateral
TOP VIEW
SIDE VIEW
Loadcell
x
z
xy
z

Experimental Setup
PIV Measurements
• Two different planes were chosen
to be measured:
– horizontal mid-span plane at
𝑧/𝐿 = −0.5, and;
– vertical centre plane at
𝑦/𝐷 = 0.
• PIV measurements were
performed in some aspect ratio
cases, namely 0.3, 0.5, 1.0 and
2.0;
• Reynolds number equal to
43,000.
z
y
x
Free-surface
plane
PIV horizontal
plane
z y
x
Free-surface
plane
PIV vertical
plane

Experimental Results
Force Measurements
• The non-dimensional forces
were evaluated for each
Reynolds condition (180s
tested):
– 𝐶 𝑥 (𝑡) =
2𝐹𝑥(𝑡)
𝜌𝐿𝐷𝑈2
– 𝐶 𝑦(𝑡) =
2𝐹𝑦(𝑡)
𝜌𝐿𝐷𝑈2
• The vortex shedding
frequency, 𝑓𝑠, was inferred
from the frequency related
to the largest peak energy
in the of the 𝐶 𝑦(𝑡):
– 𝑆𝑡 =
𝑓𝑠 𝐷
𝑈
0 20 40 60 80 100 120 140 160 180
0.5
1
1.5
Cx
Time [s]
Re = 43 000
Original Signal
Filtered Signal 0,05Hz<f<1,00Hz
0 20 40 60 80 100 120 140 160 180
-0.4
-0.2
0
0.2
0.4
Time [s]
Cy
Re = 43 000
Original Signal
Filtered Signal 0,05Hz<f<1,00Hz
• Time history of force coefficients
for cylinder with 𝐿/𝐷 = 2.0 and
Re = 43,000: (a) streamwise and
(b) transverse direction.

Force Measurements
Mean force, 𝐶 𝑥, in the streamwise
direction
• The values of 𝐶 𝑥 decrease
with decreasing aspect
ratio, except for 𝐿/𝐷 = 0.1;
• The standard deviations are
largest for the lowest aspect
ratios;
• 𝐹𝑟𝐿 = 𝑈/ 𝑔𝐿 in lowest
aspect ratio conditions are
high, 𝐹𝑟𝐿 > 0.5;
00.511.522.53
0
0.2
0.4
0.6
0.8
1
L / D
C
x
0 1 2 3 4 5
x 10
4
0
0.2
0.4
0.6
0.8
1
Reynolds Number (Re)
C
x
L / D = 2.00
L / D = 1.50
L / D = 1.00
L / D = 0.75
L / D = 0.50
L / D = 0.30
L / D = 0.20
L / D = 0.10

Force Measurements
Fluctuation force, 𝐶 𝑥 𝑟𝑚𝑠, in the
streamwise direction
• The values of non-dimensional
streamwise force fluctuation 𝐶 𝑥 𝑟𝑚𝑠
is practically constant, 𝐶 𝑥 𝑟𝑚𝑠~0.1
for cylinders with 2 ≤ 𝐿/𝐷 ≤ 0.75,
but with a decrease for 𝐿/𝐷 < 0.5;
Fluctuation force, 𝐶 𝑦 𝑟𝑚𝑠, in the
transverse direction
• The values of non-dimensional
transverse force fluctuation 𝐶 𝑦 𝑟𝑚𝑠
is practically constant,
𝐶 𝑦 𝑟𝑚𝑠~0.06 ± 0.01 for cylinders
with 2 ≤ 𝐿/𝐷 ≤ 0.75, but with a
decrease for 𝐿/𝐷 < 0.5.
00.511.522.53
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
L / D
Cyrms
00.511.522.53
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
L / D
Cxrms

Force Measurements
PSD for force in the transverse
direction
• It is possible to determine a
dominant frequency for a
cylinder with 𝐿/𝐷 = 2;
• The value of 𝑆𝑡 is pratically
constant with Reynolds
number for cylinder with
𝐿/𝐷 = 2;
• The value of 𝑆𝑡 deacreses
with increasing Reynolds
number for cylinder with
𝐿/𝐷 = 0.3;

Force Measurements
St values
• The values of 𝑆𝑡 showed a marked
decrease with decreasing aspect ratio;
• Same behavior reported by other
authors (Sakamoto & Arie (1983), Fox &
West (1993), Park & Lee (2000), Sumner
et al. (2004) and Iungo et al. (2012);
• It is interesting to note that for
𝐿/𝐷 < 0.5, it was not possible to define
a unique dominant frequency constant
with Reynolds.
• This fact is due to the three-
dimensional structures formed
downstream the cylinder for these
aspect ratio conditions, but it is possible
to note that these structures have
lower shedding frequency.
00.511.522.53
0
0.05
0.1
0.15
0.2
0.25
L / D
StrouhalNumber(St)

PIV Measurements
PIV horizontal plane at
𝑧/𝐿 = −0.5
• Contours of the mean streamwise
velocity 𝑈 𝑥/𝑈 together with
streamlines;
• The streamlines for 𝐿/𝐷 = 2.0 show
the typical picture of the flow around a
circular cylinder;
• The bubble length at mid span length
reduces significantly with the
decreasing aspect ratio;
• The effects of the free end are clearly
present already and they are much
stronger for the lowest aspect ratio
cylinder, in which the free-end effects
on the longitudinal recirculation region
distort the bubble in the horizontal
plane. For 𝐿/𝐷 = 0.3, it is difficult to
find the bubbles in the horizontal plane.
L/D = 2.0 L/D = 1.0
L/D = 0.3L/D = 0.5

PIV Measurements
PIV vertical plane at 𝑦/𝐷 = 0
• Contours of the mean
streamwise velocity 𝑈 𝑥/𝑈
together with streamlines;
• The incident flow moves
below the free-end cylinder,
separating at the leading
edge;
• Behind the cylinder, a large
longitudinal recirculation
region is observed for both
cases;
L/D = 2.0 L/D = 1.0
L/D = 0.3L/D = 0.5

PIV Measurements
Mean vorticity at horizontal
plane
• In general, the flow field in the
horizontal plane, consists of
two symmetric vortices with
positive or negative values
with respect to the wake
center plane, 𝑦/𝐷 = 0.
• The vertical vorticity, 𝜔 𝑧 𝐷/𝑈,
decreases with decreasing
aspect ratio, this fact
corroborates that the vortex
shedding diminishes in the
horizontal plane for decreasing
aspect ratio.
L/D = 2.0 L/D = 1.0
L/D = 0.3L/D = 0.5

PIV Measurements
Mean vorticity at vertical plane
• Looking at the transverse
vorticity, 𝜔 𝑦 𝐷/𝑈, the shear
layer below the free-end
cylinder is visible.
• This remains fairly steady for
approximately 0.2𝐷 below and
0.5𝐷 behind and above the
free end for all aspect ratios.
• The results showed that for
𝐿/𝐷 ≤ 0.5, the entire wake is
contaminated with three-
dimensional effects due to the
free end.
L/D = 2.0 L/D = 1.0
L/D = 0.3L/D = 0.5

General Conclusion
Force Measurements
• The forces in the streamwise direction, x,
decrease with decreasing aspect ratio, from 𝐶 𝑥~1
for 𝐿/𝐷 = 2 to 𝐶 𝑥~0.7 for 𝐿/𝐷 = 0.3.
• The forces in the transverse direction are
practically constant, 𝐶 𝑦 𝑟𝑚𝑠~0.06 ± 0.01, for
cylinders with 2 ≤ 𝐿/𝐷 ≤ 0.75.
• The higher three-dimensional behavior of the
wake is also responsible for the decrease in the
Strouhal number, from 𝑆𝑡~0.15 for 𝐿/𝐷 = 2 to
𝑆𝑡~0.05 for 𝐿/𝐷 = 0.5.

General Conclusions
PIV Measurements
• The visualizations showed two recirculation
regions: the first one below the free-end cylinder,
and the second one behind the cylinder
characterizing a recirculation bubble;
• PIV measurements in the vertical xy plane must
be performed. Results obtained by Rosetti et al.
(2013) – OMAE2013-10963, confirm the
existence of vortex with main vorticity in the
streamwise direction, that can be the source of
alternating forces for low aspect ratio cylinders
when the Von Kármán does not exist;

Think about...
Illustration of vortex tubes associated to the flow around a semi-
sphere body (Re>2,000). Source: Tamai et al. (1987).

Acknowledgments
• The authors thank Eng. Dr.
Ivan Korkischko and Eng.
César M. Freire for their
help in performing the
tests.
• The authors thank Prof. Dr.
Julio R. Meneghini for his
help in the discussions, and
to support the tests.
• The authors would also like
to acknowledge CNPq and
CAPES for the financial
support, and also PNV-USP.

THANKS
rodolfo_tg@tpn.usp.br

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OMAE2013-10454: Experimental Study on Flow Around Circular Cylinders with Low Aspect Ratio