Computers & Fluids 33 (2004) 81–96
www.elsevier.com/locate/compfluid
Large eddy simulation of turbulent flow past a square
cylinder confined in a channel
Do-Hyeong Kim a, Kyung-Soo Yang
b
a,*
, Mamoru Senda
b
a
Department of Mechanical Engineering, Inha University, 402-020 Incheon, Republic of Korea
Department of Mechanical Engineering, Doshisha University, Kyotanabe, Kyoto 610-0321, Japan
Received 23 April 2002; received in revised form 13 January 2003; accepted 13 March 2003
Abstract
Turbulent flow past a square cylinder confined in a channel is numerically investigated by large eddy
simulation (LES). The main objectives of this study are to extensively verify the experimental results of
Nakagawa et al. [Exp. Fluids 27(3) (1999) 284] by LES and to identify the features of flows past a square
cylinder confined in a channel in comparison with the conventional one in an infinite domain. The LES
results obtained are in excellent agreement with the experiment both qualitatively and quantitatively. The
well-known K
arm
an vortex shedding is observed. However, the vortices shed from the cylinder are significantly affected by the presence of the plates; mean drag and fluctuation of lift force increase significantly.
Furthermore, periodic and alternating vortex-rollups are observed in the vicinity of the plates. The rolledup vortex is convected downstream together with the corresponding Karman vortex; they form a counterrotating vortex pair. It is also revealed that the cylinder greatly enhances mixing process of the flow.
2003 Elsevier Ltd. All rights reserved.
Keywords: Turbulence; Large eddy simulation; Vortex shedding; Square cylinder
1. Introduction
Karm
an vortex shedding due to a cylindrical obstacle has been a lasting research subject for
many investigators not only for academic reasons but also for a wide variety of engineering
applications using the flow phenomenon. One of the main features of this flow configuration is a
periodic force loading in streamwise and vertical directions due to the pressure variation on the
cylinder surface caused by the periodic vortex shedding. If the loading frequency is close to the
*
Corresponding author. Tel.: +82-32-860-7322; fax: +82-32-863-3997.
E-mail address: [email protected] (K.-S. Yang).
0045-7930/04/$ - see front matter 2003 Elsevier Ltd. All rights reserved.
doi:10.1016/S0045-7930(03)00040-9
82
D.-H. Kim et al. / Computers & Fluids 33 (2004) 81–96
natural frequency of the cylindrical structure, resonance may severely damage the structure. A
number of experimental studies have been performed on this subject. Most of work has been done
on the flow past a circular cylinder rather than a rectangular one. Even though their near-wake
flow structures are expected to be topologically similar to one another, the cause of flow separation on the cylinder surfaces is totally different in the two flows. In case of the flow past a
circular cylinder, separation occurs due to adverse pressure gradient in the downstream direction,
resulting in back and forth movement of the separation point on the cylinder surface. In case of
the flow past a rectangular cylinder, however, the location of flow separation is fixed at upstream
corners of the cylinder due to the abrupt geometrical change. This feature is utilized in some
practical applications in heat and mass transfer, especially in a confined geometry. For example,
the flow analysis around a flame-holder in designing of a combustor is very important to improve
its performance [1–3].
There have been some studies on the flow past a rectangular cylinder. Davis and Moore [4]
carried out numerical investigation of the flow past a rectangular cylinder. They reported the
forces acting on the cylinder and the structure of the wake with various aspect ratios (0.6, 1 and
1.7) and angles of attack (a ¼ 0, 5 and 15) at two Reynolds numbers (Re ¼ 250, 1000) based on
mean inlet velocity and cylinder height. Especially, a detailed study was carried out for a square
cylinder (aspect ratio ¼ 1) in a wide range of Re (100–2800). Lyn and Rodi [5] also performed
experiments for the flow past a square cylinder at relatively high Re (21,400). In their study, they
focused on the shear layer formed by flow separation from the upstream corner of a square
cylinder rather than the near-wake region. Okajima [6] carried out experiments on the flow past a
rectangular cylinder of diverse aspect ratio (1, 2, 3 and 4) at various Re (70–20,000), and found the
relation between Strouhal number ðStÞ and Re. Here, the aspect ratio is defined as the ratio of
streamwise length to vertical length of a rectangular cross-section of the cylinder. It was shown
that two different patterns of vortex shedding alternately occur for the cases where aspect ratio is
larger than 1 in some range of Re.
The blockage ratios used in the studies mentioned above are less than 7.5%. In these cases, the
channel walls do not significantly affect the wake flow. On the other hand, Davis et al. [7] performed experimental and numerical investigations for the flow past a rectangular cylinder where
the cylinder was located at the center of a channel and the maximum blockage ratio was 25%. In
their study, Reynolds number (100–1850) was based on mean centerline velocity at inlet and
cylinder height; velocity profile at inlet, blockage and aspect ratios were regarded as flow parameters. It was shown that drag coefficient (CD ) increases as Re does, and recirculation regions
were noticed in the wake region near the channel walls. It should be noted that they solved twodimensional Navier–Stokes equation in their calculation. Their work was also restricted to low Re.
Nakagawa et al. [8] carried out flow measurements in similar flow configurations with various
aspect ratios; their blockage ratio was fixed as 20%. They decomposed a fluctuating flow structure
into two parts, namely, coherent structure and incoherent (turbulent) one. While the coherent
structure depends on geometric flow configuration, incoherent one is not related to geometric
constraint and completely turbulent. They showed quantitative contribution of coherent and
incoherent structures to the flow field using both phase- and time-averaging.
In this study, large eddy simulation (LES) is employed to predict the flow field in the physical configuration equivalent to that of Nakagawa et al. [8] (Fig. 1). The square cylinder is
placed at the center of the channel. The LES result is compared with the experimental data of
D.-H. Kim et al. / Computers & Fluids 33 (2004) 81–96
Inlet
83
Outlet
h
H
L
Fig. 1. Physical configuration.
Nakagawa et al. [8]. In this flow, the development of the Karman vortices downstream of the
cylinder is significantly affected by the channel walls, as Davis et al. [7] reported. Conversely, the
flow structures near the channel walls are also influenced by the Karman vortices. Instantaneous
velocity components (ui ) are decomposed into the time-averaged (Ui ), and the fluctuating (uri or u0i )
parts in Reynolds decomposition as follows:
ð1Þ
ui ¼ Ui þ uri :
When a periodic motion exists in the flow field, the fluctuating part, uri , is decomposed further into
periodic (or coherent, upi ) and turbulent (or incoherent, uti ) parts [9], respectively,
ui ¼ Ui þ upi þ uti :
ð2Þ
The phase-averaging is defined as
½ui ¼ Ui þ upi :
ð3Þ
In addition, a detailed investigation on the mutual influence between the cylinder and the channel
walls is carried out by flow visualization using Lagrangian particle tracking technique. To identify
any difference between the flow around a rectangular cylinder confined in a channel and a
counterpart in an open domain, an additional simulation is performed without walls, and CD , St,
turbulent kinetic energy and wake profiles are compared between the two.
2. Formulation
In this work, three-dimensional incompressible continuity and momentum equations are used
as governing equations and all equations are filtered by a box filter,
o
uj
¼ 0;
oxj
i
o
ui oð
ui oP
o
1 o2 u
uj Þ
þ
¼
sij þ
oxj
oxi oxj
Re oxj oxj
ot
ð4Þ
ði ¼ 1; 2; 3Þ:
ð5Þ
Here, the index i represents each direction in the Cartesian coordinate system; P and sij mean
filtered pressure and subgrid-scale stress components, respectively. All variables are normalized by
the mean inlet velocity (Um ) and the cylinder height (h). Finite volume method is employed to
discretize the governing equations, and a fractional-step method [10] is used to advance them in
time. Nonuniform staggered grid is applied in the Cartesian coordinate system. Fig. 2 shows the
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D.-H. Kim et al. / Computers & Fluids 33 (2004) 81–96
Fig. 2. Grid system.
grid system on an x–y plane. The grid spacing in the immediate vicinity of the cylinder is 0:01h.
The grid was refined until all the statistics reported in this paper (up to second order statistics)
showed little dependence on grid resolution. It turns out that 224 · 144 · 64 cells are adequate in
streamwise (x1 or x), normal (x2 or y) and spanwise (x3 or z) directions, respectively. Subgrid-scale
modeling is very important in LES. A dynamic subgrid-scale model [11] is employed to reflect the
effects of subgrid-scale eddies on larger ones. A detailed implementation about subgrid-scale
modeling used in this study can be found in Yang and Ferziger [12].
3. Flow parameters
In this work, Re based on h and Um is fixed as 3000, and the blockage ratio is 20%. The
spanwise size of the computational domain is equal to h and periodic boundary condition is
applied in that direction. Uniform velocity profile with a thin boundary layer thickness (6% of
channel height (H )) is imposed as an inlet boundary condition. To obtain the inlet velocity profile,
a separate simulation is performed for a developing channel flow. The velocity profile at the
streamwise location with the boundary layer thickness mentioned above is taken and jittered by
random numbers of 6% of Um in root-mean-squared (RMS) magnitude. At outlet, a convective
condition [13] is employed:
of
of
þ Uconv
¼ 0;
ð6Þ
ot
ox
where Uconv is the mean velocity at outlet and f is any physical variable convected out through the
outlet. For the flow fields considered here, f represents velocity components (ui ) in each direction.
No-slip condition is imposed at all solid walls.
4. Results
4.1. Time-averaged flow fields
Velocity components and turbulent fluctuations are averaged both in time and in the spanwise
direction (h i), and compared with the experimental results of Nakagawa et al. [8]. To indicate
D.-H. Kim et al. / Computers & Fluids 33 (2004) 81–96
85
Fig. 3. Mean velocity profile along the centerline (j: Nakagawa et al.Õs [8] experiment, ––: present): (a) streamwise
component and (b) normal component.
duration of time needed for time-averaging, flow-through time (FTT) which means the ratio of
streamwise domain length (L) to Um is introduced as a normalized time scale. In this study, timeaveraging is performed for 6.3 FTT after the initial transient period. Fig. 3 presents profiles of
mean streamwise and normal velocity components along the centerline (y ¼ 0). The x coordinate
is measured from the downstream face of the square cylinder. Fig. 3(a) reveals excellent agreement
with experimental measurements by Nakagawa et al. [8]. The LES results cannot be verified near
the downstream face of the cylinder because the experimental data are not available there.
However, the present results show good prediction about the size of recirculating region and the
magnitude of reversed velocity. Fig. 3(b) exhibits distribution of mean normal velocity. Since
geometry and boundary conditions are symmetric in the normal direction (y), the averaged
normal velocity must vanish along the centerline as shown in Fig. 3(b).
Streamlines of the averaged flow field are shown in Fig. 4. A pair of counter-rotating vortices is
identified downstream of the obstacle. Other recirculating regions are also observed near the
upper and lower faces of the square cylinder; that is not the case in the flows past a circular
cylinder. It is also revealed that the flow separated at the leading edge is not reattached to the wall.
Fig. 4. Streamlines of time and space(z) averaged velocity field.
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D.-H. Kim et al. / Computers & Fluids 33 (2004) 81–96
Profiles of mean velocities, turbulent fluctuations and Reynolds stress are shown in Figs. 5–9 at
x=h ¼ 1, 3.5, 6.0 and 8.5, respectively. Only half profile is shown due to the symmetry in y. Good
agreement with the experiment is noticed in Figs. 5 and 6 for streamwise and normal mean velocity profiles. In Fig. 5, it is observed that momentum defect near the downstream face of the
Fig. 5. Profiles of mean streamwise velocity (j: Nakagawa et al. [15], ––: present): (a) x=h ¼ 1:0, (b) x=h ¼ 3:5,
(c) x=h ¼ 6:0 and (d) x=h ¼ 8:5.
-0.5
-0.5
-0.5
-0.5
-1
-1
-1
-1
y/ h
0
y/h
0
y/h
0
y/h
0
-1.5
-1.5
-1.5
-1.5
-2
-2
-2
-2
-2.5
(a)
<v>/U m
0.5
0
(b)
-2.5
-2.5
-2.5
0
<v>/U m
0
0.5
(c)
<v>/U m
0
0.5
(d)
0.5
<v>/U m
Fig. 6. Profiles of mean normal velocity (j: Nakagawa et al. [15], ––: present): (a) x=h ¼ 1:0, (b) x=h ¼ 3:5,
(c) x=h ¼ 6:0 and (d) x=h ¼ 8:5.
Fig. 7. Profiles of RMS streamwise velocity fluctuation (j: Nakagawa et al. [15], ––: present): (a) x=h ¼ 1:0,
(b) x=h ¼ 3:5, (c) x=h ¼ 6:0 and (d) x=h ¼ 8:5.
D.-H. Kim et al. / Computers & Fluids 33 (2004) 81–96
87
Fig. 8. Profiles of RMS normal velocity fluctuation (j: Nakagawa et al. [15], ––: present): (a) x=h ¼ 1:0, (b) x=h ¼ 3:5,
(c) x=h ¼ 6:0 and (d) x=h ¼ 8:5.
Fig. 9. Profiles of Reynolds stress (j: Nakagawa et al. [15], ––: present): (a) x=h ¼ 1:0, (b) x=h ¼ 3:5, (c) x=h ¼ 6:0 and
(d) x=h ¼ 8:5.
cylinder is quickly recovered in the downstream direction. It can be seen from Fig. 6(a) that the
profile of mean normal velocity near the cylinder is much affected by the pair of vortices formed
behind the cylinder. The other figures show little influence by the pair of vortices away from the
cylinder. It should be noted that the numerical results well predict the recovery of the velocity in
the wake region where it is generally known that the behavior of the flow is sensitive to small
changes in the parameters. While profiles of streamwise turbulent fluctuation show some disagreement with the experimental results except near the walls in Fig. 7, profiles of normal turbulent fluctuation show good agreement with the experimental measurements in Fig. 8. Moreover,
the maximum magnitude of normal turbulent fluctuation is larger than that of streamwise turbulent fluctuation near the cylinder (Fig. 7(a) and Fig. 8(a)). From this, one can conclude that the
vortices generated in the vicinity of the upper or lower faces of the cylinder cause intense momentum transfer in the vertical direction. Profiles of Reynolds stress are presented in Fig. 9 and
show excellent agreement with the experimental data at all streamwise locations. It can be noticed
that the Reynolds stress is affected mainly near the cylinder like the mean normal velocity. A
supplementary simulation for an infinite-domain case was performed using a grid system of
240 · 192 · 64 with a domain size of 30h 20h h. In Fig. 10, streamwise mean velocity profiles in
the channel are compared with those in an infinite domain at the same Re. It is shown that the free
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D.-H. Kim et al. / Computers & Fluids 33 (2004) 81–96
Fig. 10. Profiles of streamwise mean velocity (- - -: confined domain, ––: infinite domain): (a) x=h ¼ 1:0, (b) x=h ¼ 3:5,
(c) x=h ¼ 6:0 and (d) x=h ¼ 8:5. In both cases, Re is identical.
wake is significantly restricted by the wall. The flow in the center region of the channel is faster
than the counterpart in the infinite domain. However, the mean velocity gradient is nearly
identical in the center regions of the two cases. To examine distribution of turbulence around the
square cylinder, streamwise and normal turbulent fluctuations and turbulence intensity are presented in Fig. 11. The maximum intensity is located at approximately 1h downstream of the
cylinder. In that region, entrainment of vortices and recirculation of flow occur. Thus intense
mixing is expected. Fig. 12 shows square root of turbulent kinetic energy normalized by Um along
the centerline. One can observe that the magnitude increases towards the cylinder and that the
flow is significantly affected by the cylinder.
Comparison of turbulence intensity with that around a square cylinder in an infinite domain at
the same Re is shown in Fig. 13. It is observed that the contour shapes of the maximum region are
different. In the case with an infinite domain, the local maximum regions of streamwise velocity
fluctuation behind both trailing edges such as shown in Fig. 11(a), do not exist. This fact suggests
that the channel has a positive effect on spreading high streamwise turbulent fluctuation in the
normal direction in the near-wake region.
Fig. 14 presents distribution of the mean wall-shear stress on the channel wall to indicate the
effect of the square cylinder on the stress. It is shown that the maximum value occurs at
x=h ¼ 0:8 where the flow is accelerated due to reduction of the cross-sectional area. On the other
hand, the minimum occurs at the location where flow separation takes place in order to generate a
vortex counter-rotating against the K
arm
an vortex shed from the square cylinder. This will be
more clear in the flow visualization shown later. Due to adverse pressure gradient, normal gradient of the mean streamwise velocity on the channel wall becomes smaller compared with those
at the other locations.
Fig. 15 presents distributions of the mean streamwise velocity near the channel wall at selected
downstream locations in wall unit. It is revealed that the thickness of viscous sublayer is thinner
than that of equilibrium boundary layer; this is similar to the result of DavenportÕs [14] experiment on an abruptly expanded circular pipe flow. DavenportÕs experiment showed that thinner
viscous sublayers were noticed close to the wall in the recirculation region. It was also reported
that thickness of viscous sublayer is recovered further downstream, where the flow is redeveloped.
These observations also hold for the current flow. See Fig. 15.
D.-H. Kim et al. / Computers & Fluids 33 (2004) 81–96
89
Fig. 11. Contour plots of RMS turbulent fluctuations and turbulence intensity (increment: 0.08): (a) streamwise turbulent fluctuation, (b) normal turbulent fluctuation and (c) turbulence intensity.
Fig. 12. Normalized turbulent kinetic energy distribution upstream of the square cylinder along the centerline.
4.2. Phase-averaged flow fields
Phase-averaging was carried out using lift force acting on the cylinder as the phase reference. A
set of 22 phase bins was used for one cycle period. The number of flow fields belonging to each
phase bin is about 30, which is much smaller than Nakagawa et al.Õs [8]. However, it turns out that
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D.-H. Kim et al. / Computers & Fluids 33 (2004) 81–96
0.3
0.1
0.4
0.5 0.9 0.6
0.7
1.2
0.2
0.3
0.1
0.9
1.1
0.8
0.8
0.4
1.0
0.7
0.6
0.5
(a)
0.4
0.3
0.2
0.5
0.6
0.1
0.9
1.0
0.7
0.8
0.6
0.2
0.7
0.3
0.6
0.5
0.4
(b)
0.1
Fig. 13. Comparison of turbulence intensity (hu0i u0i i=Um2 , increment: 0.1): (a) square cylinder in the channel and (b)
square cylinder in an infinite domain.
Fig. 14. Mean shear stress distribution along the plate.
streamwise and normal coherent velocity and incoherent turbulent kinetic energy (kt ) for each
2
2
phase are consistent with their experiment. See Fig. 16. Here, kt is defined as ðhut i þ hvt iÞ=2, and
the abscissa constitutes one period (2p). Streamlines in the flow field for selected phases (1, 6, 11,
16, 21) are presented in Fig. 17.
4.3. Instantaneous flow fields
To effectively investigate time-dependent features of the complicated flow fields around the
square cylinder, passive-particle tracking technique was used. The particles were released at even
D.-H. Kim et al. / Computers & Fluids 33 (2004) 81–96
91
Fig. 15. Profiles of mean streamwise velocity near the channel wall at various streamwise (x) locations downstream of
square cylinder in wall-unit. Here, rþ denotes the distance from the channel wall.
Fig. 16. Variations of coherent velocity components and incoherent turbulent kinetic energy with phase at x=h ¼ 1:5
and y=h ¼ 1:5: (a) coherent streamwise velocity component, (b) coherent normal velocity component and (c) incoherent turbulent kinetic energy (: Nakagawa et al. [8], j: present).
time intervals. Fig. 18(a) shows an instantaneous snap shot of the experiment using hydrogen
bubbles and the figure is compared with the present result (Fig. 18(b)) at the same phase. Flow
structures around the square cylinder and downstream up to x=h ¼ 8 reveal good agreement with
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D.-H. Kim et al. / Computers & Fluids 33 (2004) 81–96
Fig. 17. Streamlines: (a) phase 1, (b) phase 6, (c) phase 11, (d) phase 16 and (e) phase 21.
Fig. 18. Flow visualization: (a) experiment [15] using hydrogen bubbles and (b) current simulation using passive
particles.
each other. Further downstream, small discrepancy is noticed between the figures. However, in
spite of less numerical resolution in the far downstream region, flow structures there are at least
consistent with the experimental visualization.
Fig. 19 shows a series of snap shots of the passive-particle simulation; the particles are released
on the planes at the center (y=h ¼ 0) and at Dy=h ¼ 0:05 away from each channel wall, to find how
the wall affects K
arm
an vortices convected downstream. In the figures, vortical structures shed
from the cylinder are clearly observed and the particles released on the center plane pass over the
D.-H. Kim et al. / Computers & Fluids 33 (2004) 81–96
93
Fig. 19. Sequential plots of passive particles: (a) t ¼ T1 , (b) t ¼ T1 þ 0:23T , (c) t ¼ T1 þ 0:47T and (d) t ¼ T1 þ 0:70T ,
where T is the period of vortex shedding.
top or bottom faces of the square cylinder alternately. The vortices shed from the cylinder move
downstream in a confined manner due to restriction by the channel walls and induce secondary
vortices close to each wall, resulting in a pair of counter-rotating vortices moving downstream
together at the same rate. The induced vortex is smaller in size than the one shed from the square
cylinder. This phenomena are repeated periodically on each channel wall.
Fig. 20 is an instantaneous snap shot which shows separation on the lower wall in a perspective
view; the flow separates and subsequently breaks down. Fig. 21 shows traces of the particles
Fig. 20. Passive-particle simulation showing separation on the lower wall.
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D.-H. Kim et al. / Computers & Fluids 33 (2004) 81–96
Fig. 21. Distribution of passive particles around the cylinder.
released at 0:1h downstream of the upper leading edge of the cylinder, and at 0:1h away from the
top face of the square cylinder. It is clearly observed from the figure that vortices are developed
and convected downstream. In Fig. 21, the particles are released close to the top face of the
cylinder, and they move into the region even near the bottom face of the cylinder; this demonstrates how complicated the flow pattern is around the square cylinder. This figure also confirms
that the square cylinder can significantly enhance mixing in channel flow.
Characteristics of wakes are compared in Table 1 for the two flow conditions. The Strouhal
number based on the frequency of lift force, the height of cylinder (h) and the mean streamwise
velocity at the cylinder location is 0.124, consistent with Nakagawa et al.Õs [8] 0.13, while St of the
infinite-domain case based on the height of cylinder (h) and the mean streamwise velocity at inlet
is 0.125, consistent with OkajimaÕs (0.126) [6]. Drag coefficient for a square cylinder has been
reported by a number of authors. For an infinite domain, White [16] reported 2.1 for Re P 104 ,
and Davis and Moore [4] reported 2.2 at Re ¼ 2800 in their numerical study. In case of a square
cylinder confined in a channel, Davis et al. [7] reported 2.20 and 2.52 for 16% and 25% blockage
ratios, respectively at Re ¼ 1850; their results were numerically computed using experimental inlet
velocity profiles. One can notice that the values of present drag coefficients are consistent with
those of the previous studies. For convenienceÕ sake, the comparisons of St and CD mentioned
above are summarized in Tables 2 and 3. From Table 1, it can be inferred that at the same Re, a
square cylinder confined in a channel experiences bigger drag force, larger lift fluctuation and
larger St than a square cylinder in an infinite domain does. It should be noted that St for the
confined cylinder is increased if it is recalculated using the mean velocity at inlet. These trends
about drag force and St are consistent with Davis et al.Õs [7]. Furthermore, the streamwise length
Table 1
Comparison of characteristics of wakes for simulations with the two conditions, Re ¼ 3000
St
CDmean
CDrms
CLrms
Lr =h
Confined in a channel
(20% blockage ratio)
0:124 f Uhb
2.76
0.49
2.06
0.67
Infinite domain
0:125 f
1.97
0.43
1.15
0.96
h
Um
Here, Lr is the length of recirculating region behind the square cylinder, and CDrms and CLrms represent RMS fluctuations
of CD and CL , respectively. Ub is the mean streamwise velocity at the cylinder location. CD and CL are based on Um .
D.-H. Kim et al. / Computers & Fluids 33 (2004) 81–96
95
Table 2
Comparison of Strouhal numbers
Author
Confined channel
Nakagawa et al. [8]
Present f Uhb
Okajima [6] f Uhm
Present f Uhm
Infinite domain
f
h
Ub
St
0.13
0.124
0.126
0.125
Table 3
Comparison of drag coefficients
Davis and Moore [4]
Davis et al. [7]
White [16]
Present
CD
Re
Blockage ratio
2.2
2.20
2.52
2.1
2.76
1.97
2800
1850
1850
Re P 104
3000
3000
Infinite domain
16%
25%
Infinite domain
20%
Infinite domain
of the recirculating region behind a square cylinder (Lr ) is reduced in the presence of channel
walls. As noticed in Fig. 3, Lr =h obtained by Nakagawa et al. [8] is 0.60 which is slightly smaller
than the present numerical value (0.67).
5. Conclusion
In this study, LES is employed to predict turbulent flow fields past a square cylinder confined in
a channel with a blockage ratio of 20% and at Re ¼ 3000. Time-averaged LES results are in good
agreement with the experiment currently available. Periodic and alternating vortex shedding
which typically occurs in obstructed flows is also observed. Existence of channel walls, however,
reduces the size of the recirculating region behind the square cylinder, and induces bigger drag
force and larger lift fluctuations on the square cylinder compared with those in the corresponding
infinite-domain case. The Strouhal number of vortex shedding also increases by the presence of
the channel walls.
Normal turbulent fluctuation is larger than streamwise one in the region near the downstream
face of the cylinder. Phase-averaging is used to investigate the coherent structures, and comparison with the experiment shows good agreement. To examine the progress of the flow in time,
passive-particle tracking technique is employed. The wake region downstream of the cylinder is
restricted by the channel and gives rise to change of flow structures near the channel walls. When a
vortex shed from the cylinder approaches one of the channel walls, the vortex induces a counterrotating vortex originating from the wall. The two vortices are convected downstream at the same
speed, and finally dissipated. This occurs near each channel wall periodically and alternately. The
particle-tracking simulation also reveals active mixing around the square cylinder.
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D.-H. Kim et al. / Computers & Fluids 33 (2004) 81–96
Acknowledgements
This work was supported by Inha University Research Grant (INHA-21959). The authors are
grateful to Dr. Nakagawa at Department of Mechanical Engineering, Aoyama Gakuin University
for useful discussion during this research.
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