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Journal of Wind Engineering
and Industrial Aerodynamics 88 (2000) 231–246
Free end effects on the near wake flow structure
behind a finite circular cylinder
Cheol-Woo Park, Sang-Joon Lee*
Department of Mechanical Engineering, Pohang University of Science and Technology,
Pohang 790-784, South Korea
Abstract
The free end effect on the near wake of a finite circular cylinder in a cross flow has been
investigated experimentally. Three finite cylinders with aspect ratios (L=D) of 6, 10 and 13
were tested in a subsonic wind tunnel at a Reynolds number of 20000. A hot-wire anemometer
was employed to measure the wake velocity. Mean pressure distributions on the cylinder
surface were also measured. The flow near the free end was visualized to observe the flow
structure qualitatively in a circulating water channel. The experimental results from these finite
cylinder (FC) models were compared with those of a two-dimensional circular cylinder. The
flow past the FC free end shows a complicated three-dimensional wake structure. As the FC
aspect ratio decreases, the vortex shedding frequency is decreased and the vortex formation
region is elongated. The free end effect becomes dominant close to the FC free end. The three-
dimensionality of the FC wake may be attributed mainly to the strong entrainment of
irrotational fluids, caused by the downwash of counter-rotating vortices separated from the
FC free end. The downwash flow is concentrated in the central region of the wake. A peculiar
flow structure having a 24Hz frequency component was observed near the free end using
spectral analysis and cross-correlation of the velocity signals. This 24Hz frequency component
is closely related to the counter-rotating twin vortices formed near the FC free end.
# 2000 Elsevier Science Ltd. All rights reserved.
Keywords: Finite cylinder; Free end; Aspect ratio
*Corresponding author. Tel.: +82-54-279-2169; fax: +82-54-279-3199.
E-mail address: sjlee@postech.ac.kr (S.-J. Lee).
0167-6105/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.
PII: S016 7- 6105(0 0)00051 -9
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1. Introduction
Flow around a circular cylinder has been extensively investigated in the past due
to its simple geometry and coherent vortex structure. A circular cylinder is a
representative bluff body, showing two-dimensional (2-D) flow characteristics. At
low Reynolds numbers, three-dimensional (3-D) flow characteristics consisting of
altered flow structures in the axial direction are frequently observed in the vortices
shed from a 2-D circular cylinder.
This three dimensionality has been attributed to non-uniformities that exist in the
flow and along the body span, and to the particular end constraints imposed in the
experimental arrangement. The various end constraints on the wake structure have
been investigated by Slaouti and Gerrard [1].
Williamson [2] found a discontinuity in the Strouhal–Reynolds number relation-
ship for oblique vortex shedding at low Reynolds numbers. He suggested that the
critical Reynolds number could be affected by differences in the flow non-uniformity,
end conditions, or the free stream turbulence level.
In the strict sense, the cylinder wake has 3-D flow characteristics over all Reynolds
number ranges. In the near-wake region behind a 2-D circular cylinder, however, the
three dimensionality is weak, because vortex shedding is regular and parallel to the
cylinder axis in the vortex formation region. Therefore, the cylinder wake has been
assumed a 2-D flow in view of the coherent vortex structure. The Strouhal number
does not change along the cylinder axis if appropriate end plates and a small aspect
ratio are used (see Ref. [3]). Baban et al. [4] demonstrated that for a 2-D cylinder in a
cross-flow, vortex shedding is truly 2-D, and the strength of the roll-up vortices is
fairly uniform along the span.
The main causes for flow three dimensionality include the non-uniformity of free
stream flow, the presence of longitudinal vortices and a low aspect ratio (L=D) of the
cylinder. The aspect ratio is the ratio of cylinder height L to diameter D. The free end
of a finite cylinder (FC) is a direct and significant factor for flow three
dimensionality. Many high-rise bluff bodies and tall buildings can be simplified as
a finite cylinder with a free end. The free end changes the flow structure in the near
wake, including the vortex formation region, vortex-shedding pattern and surface
pressure distribution. Parallel vortex shedding can be introduced through modifica-
tion of the cylinder ends, as shown by Eisenlohr and Eckelmann [5].
Wieselsberger [6] investigated the 3-D flow characteristics of a finite circular
cylinder mounted on a flat plate. The drag force acting on the cylinder decreased at
small aspect ratios. Baban et al. [7] observed an increase in drag force fluctuations
due to highly turbulent re-circulation flow in the wake region, especially in the shear
layer separated from the end of the cylinder. Budair et al. [8] found that vortex
shedding disappeared at a Reynolds number Re=15000 when the FC aspect ratio
(L=D) was lower than 7. Sakamoto and Arie [9] revealed that the vortex-shedding
pattern was largely dependent on the FC aspect ratio. Okamoto and Sunabashiri [10]
found that the wake behind finite cylinders of small aspect ratio (L=D ¼ 1–2) was
symmetric, but that the wake pattern became 3-D when the aspect ratio was larger
than L=D ¼ 4.
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However, there are still some contradictions about the three dimensionality of the
FC wake, especially for high Reynolds number flows. Farivar [11] investigated the
effect of the FC free end on the mean pressure, pressure fluctuation, and drag force
acting on a cylinder when exposed to a uniform flow. He observed that the vortex-
shedding frequency disappeared for aspect ratios smaller than L=D ¼ 7:5. On the
other hand, Zdravkovich et al. [12] noted vortex shedding in the FC wake around an
aspect ratio of L=D ¼ 2, although it was irregular and intermittent.
In previous studies, the flow past a finite cylinder at high Reynolds numbers,
particularly in the vicinity of the free end, was not fully investigated. Therefore, this
study investigates the effect of FC aspect ratio on near-wake flow characteristic,
especially near the free end.
2. Experimental apparatus and methods
The experiments were carried out in a closed-return-type subsonic wind tunnel,
with a test section of 0.72m wide?0.6m high?6m long. Free-stream turbulence
intensity in the test section was less than 0.08%. Free-stream velocity was fixed at
10m/s, and the corresponding Reynolds number based on the cylinder diameter
(D ¼ 30mm) was 20000. A schematic diagram of the experimental setup and
coordinate system is shown in Fig. 1.
In this study, three FC models with different aspect ratios (L=D ¼ 6; 10; 13) were
tested. For comparison, a 2-D circular cylinder with an aspect ratio of L=D ¼ 17:3,
with no gap between the free end and test section ceiling, was also tested. The
experimental models were made of stainless-steel rod and their surfaces were
polished smooth using sandpaper. The finite cylinder was installed vertically on a 15-
mm-thick flat plate, with a sharp-edged leading edge of angle 308. The FC model was
placed 0.5m downstream from the leading edge of the flat plate. In order to avoid
flow-induced vibrations, the natural frequencies of the FC models were set to be
greater than 20 times the vortex-shedding frequency.
The boundary layer that developed on the sharp-edged flat plate was about
4.1mm thick at the location of the cylinder. A horseshoe vortex could be formed at
the junction between the FC models and the ground plate. However, since the
measurements were performed in the upper half of the wake, from mid-height to the
free end of the cylinder, the effects of the wall boundary layer and horseshoe vortex
were negligible.
West and Apelt [13] found that the pressure distribution around a circular cylinder
varies only slightly with respect to blockage ratio. For blockage ratios of less than
6%, the Strouhal number is independent of the blockage ratio and the aspect ratio of
the cylinder. Since the maximum blockage ratio for the 2-D cylinder model was
4.2%, the blockage effect has not been considered in this study.
The wake velocity was measured using an I-type hot-wire probe (DANTEC
55P11) connected to a constant temperature hot-wire anemometer (TSI IFA 100).
The hot-wire probe was maneuvered to the measuring points using a 3-D traverse
system with an accuracy of 0.01mm. At each measurement point, 32000 velocity
C.-W. Park, S.-J. Lee / J. Wind Eng. Ind. Aerodyn. 88 (2000) 231–246233
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Fig. 12. Cross-correlation function of velocity signals having the 24Hz frequency component at
Y=D ¼ ?2 for the finite cylinder of L=D ¼ 13 ðX=D ¼ 3; Z=L ¼ 0:95Þ.
Fig. 13. Comparison of mean pressure coefficient distributions around the free end of L=D ¼ 10 cylinder.
C.-W. Park, S.-J. Lee / J. Wind Eng. Ind. Aerodyn. 88 (2000) 231–246245
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4. Conclusion
The effect of a finite cylinder (FC) free end in a cross flow on near-wake flow
characteristics was investigated experimentally. The three dimensionality of the FC is
attributed to the counter-rotating twin vortices separated from the FC free end. The
downwash flow is concentrated on the central region of the wake. From spectral
analysis and cross-correlation of the velocity signals, a peculiar flow structure having
a 24Hz frequency component was observed near the free end. This 24Hz frequency
component seems to be closely related to the counter-rotating twin vortices formed
near the FC free end.
The vortex shedding frequency decreases and the vortex formation region
increases as the FC aspect ratio decreases. The vortex formation region and periodic
vortex shedding disappear very close to the free end. This is caused by the twin
vortices descending from the free end, which interact with the regular vortices shed
from the two sides of the cylinder.
Acknowledgements
The authors thank the BK21 project for its contribution.
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