Simulation of Flow around a Surface-mounted
Square-section Cylinder of Aspect Ratio Four
You Qin Wang1, Peter L. Jackson2 and Jueyi Sui2
1
High Performance Computing Laboratory, College of Science and Management, the University
Of Northern British Columbia, Prince George, BC, Canada V2N 4Z9
2
Environment Science & Engineering Program, College of Science and Management, the University
Of Northern British Columbia, Prince George, BC, Canada V2N 4Z9
Email: [email protected]
The Reynolds Stress Model (RSM) and Detached
Eddy Simulation (DES) are used to study the
turbulent flow around a surface-mounted square
cylinder of aspect ratio h/d=4 at a Reynolds number
of 13,041. The performances of the RSM and DES
are evaluated by comparing their simulation results
against experimental measurements. Both models
successfully reproduced the primary flow, as well as
the three-dimensional large-scale vortex structure in
the wake of finite wall-mounted body. However,
RSM produces better predictions in both mean
velocity and root-mean-square velocity than DES.
The Strouhal number obtained by statistical analysis
of the streamwise drag coefficient on the top wall of
the cylinder is 0.1 by RSM, which matches the value
obtained by experimental study carried out under a
similar flow condition with the same geometry.
investigations have been done for the h/d >1 case.
Becker et. al. [12] have studied the case with h/d=6 at
Reynolds number of 1.25x104. However, very limited
information about their numerical approach and
numerical solution has been provided in their
published work. Recently LES was used to study the
turbulent flow around a surface-mounted square
cylinder of aspect ratio h/d = 3 and 5 at a relatively
low Reynolds number of Re=500 by Einian et. al.
[13]-[15]. In the present study, both RSM and DES
were used to simulate the flow around a surfacemounted square cylinder of aspect ratio h/d = 4 at
Reynolds number of Re=13041. The goal of this
work is to evaluate the performance of these two
models and to search for a numerical approach which
could provide a reasonably accurate prediction of
flow characteristics. The detailed information from
simulations
can
complement
experimental
measurements to improve fundamental understanding
of the flow structure and dynamics.
1. INTRODUCTION
2. SIMULATION OVERVIEW
The flow around an infinite square cylinder has a
two-dimensional nature and is typically characterized
by von Karman vortex shedding [1]. In contrast to the
infinite case, the flow behind a surface-mounted
square cylinder is more complex since the wake is
characterized by the interaction of three types of
vortices, namely, tip vortices, spanwise vortices and
horseshoe vortices. Turbulent flow around a wallmounted cube [1]-[7] has received more attention
than the flow around a surface-mounted square
cylinder of aspect ratio h/d >1. Wang et. al. [8]-[9]
have reported an experimental study with h/d ranging
from 3-7. Meanwhile, experimental investigation
conducted by Bourgeois [10]-[11] focused on one
aspect ratio of h/d=4. So far, only a few numerical
In the following section, the computational grid and
domain, numerical method, and the boundary
conditions are summarized. More detailed
information regarding both RSM and DES used in
the present study can be found in [16]-[17].
ABSTRACT
The problem under consideration involves flow over
a surface-mounted square cylinder of aspect ratio
h/d=4 in an open-section wind tunnel. The study case
was originally posted at the 20th Annual Conference
of the Computational Fluid Dynamics Society of
Canada (CFD2012) as a challenge exercise. The
experimental results obtained by Particle Image
Velocimetry (PIV) were provided by Bourgeois et. al.
[10]-[11] for code validation and performance
assessment. The calculations were performed at a
Reynolds number of 13,041 based on the width of
square cylinder d and free-stream velocity U∞, using
the computational fluid dynamics code FLUENT
(fluent 6.2.16). The simulation domain was set to be
0.762m x 0.1778m x 0.127m, and the free stream
turbulence intensity was set at 0.8%, the same as in
the experimental set up. The no-slip boundary
condition was used at the bottom edge, and the
symmetrical condition was used at the top edge, and
both side edges. A pressure-outlet boundary
condition was used to define the static pressure at the
flow outlet. The grid consists of 487,085 cells with a
maximum volume of 8.70 x 10-8 m3, and it was
generated having a thin boundary layer around the
cylinder walls. A segregated solution approach using
the SIMPLE algorithm was used. At least 4000 time
steps were used to obtain the time-averaged results,
and convergence was declared when the maximum
scaled residuals were less than 10-4 for the velocity
equations, and 10-3 for all other equations.
of two foci by RSM. Figs 2-4 indicate that the results
obtained by RSM match well with the experimental
measurements, including the dipole-type mean
streamline pattern at mid-span, the characteristic of
low aspect ratio obstacles.
(a) DES
3. RESULTS AND DISCUSSION
Selected results obtained by both RSM and DES are
presented in Figs. 1-8 below. Fig. 1 shows the timeaveraged streamlines in a symmetry plane parallel to
the approach flow located at the centerline of the
cylinder with the contour of the mean streamwise
velocity. Notably, RSM reproduced better prediction
in the mean streamwise velocity and time-averaged
streamlines than DES did. The saddle point marked
by the symbol ‘+’ in the Figs. 1(b) and 1(c) results
from interaction between downwash and upwash
flows. This type of saddle point often occurs when
the aspect ratio h/d is sufficient large such that the
flow over the top of the square cylinder does not
attach to the ground surface. The time-averaged
streamlines plotted in Fig. 1(a) shows that there is an
absence of appreciable upwash flow from the ground
plane; this is consistent with the flow around a finite
cylinder of low aspect ratio, i.e., where h/d is less
than the critical value [15].
Figs. 2 and 3 show the time-averaged streamlines and
mean steamwise velocity contours in two different
horizontal sections of the wake behind the square
cylinder. At z/d=1.0, the recirculation zone behind
the square cylinder obtained by DES is larger than
the recirculation zones obtained by RSM and PIV. In
fact, the results obtained by DES indicate that the
wake tends to become larger and stronger near the
lower half of the cylinder. At z/d=2.0, an important
difference in the streamline patterns obtained by DES
and RSM is that there are four foci by DES, instead
(b) RSM
(c) PIV solutions from [10]
Figure 1. Comparison of mean streamwise velocity
and the time-averaged streamline at y/d=0.
Mean velocity and root-mean-square velocity
obtained by DES and RSM at z/d=2.0, and y/d=0.0877 are compared with PIV solutions in Fig. 4. It
is observed that although both models underpredicted
the root-mean-square streamwise velocity, overall
RSM produced better predictions in both mean
velocity and root-mean-square velocity than DES,
especially for the root-mean-square spanwise
velocity.
(a) DES
(a) DES
(b) RSM
(b) RSM
(c) PIV solutions from [10]
(c) PIV solutions from [10]
Figure 2. Comparison of mean velocity at
z/d=1.0.
Figure 3. Comparison of mean velocity at
z/d=2.0.
(a) Streamwise mean velocity
(b) Spanwise mean velocity
Instantaneous streamlines and instantaneous vertical
vorticity contours in three different horizontal
sections obtained by both DES and RSM are plotted
in Fig. 5 and Fig. 6, respectively. The stream-ribbons
of the instantaneous velocity obtained by both DES
and RSM are plotted in Fig. 7. The plots indicate that
the flow structure predicted by RSM is highly threedimensional due to the interaction of the downwash
flow, upwash flow and the spanwise vortex shedding.
However, near the upper half of the cylinder, flow
structure predicted by DES is dominated by
downwash flow, and the axis of the back vortex is
almost parallel to the y axis (the spanwise
coordinate).
The frequency spectra of the streamwise drag force
coefficient is shown in Fig. 8. The drag coefficient
was taken on the top wall of the square cylinder and
the frequency has been converted to a Strouhal
number. The Strouhal number obtained by RSM is
0.1 which is consistent with the experimental
observations [10]. Two Strouhal numbers are
obtained by DES. In the power spectrum distribution,
the first peak is 0.05, and the second peak is 0.1, its
harmonic.
4. CONCLUSIONS
(c) Root-mean-square streamwise velocity
The DES and RSM in FLUENT were used to predict
the flow around a surface-mounted finite square
cylinder at Reynolds number of 13041. Overall, the
predicted mean velocity and turbulence quantities in
the present study are in good agreement with
measurement data provided by CFD society of
Canada (http://www.cfdcanada.ca/challenge/data), as
well as reported in the literature [10]-[11]. RSM
produces better predictions than DES of both mean
velocity and root-mean-square velocity. It captured
most flow features including the vortex shedding
frequency. The numerical solutions indicate that the
flow behind the square cylinder is surprisingly
complex. It is highly three-dimensional due to the
interaction of the downwash flow, upwash flow and
the spanwise vortex shedding.
ACKNOWLEDGEMENTS
(d) Root-mean-square spanwise velocity
Figure 4. Mean and root-mean-square
velocity profiles at z/d=2.0.
Computing infrastructure for this work was provided
by grants from the Canada Foundation for
Innovation, BC Knowledge Development Fund, SGI
Canada and donors to the University of Northern
British Columbia.
(a) z/d=1.0
(b) z/d=2.0
(c) z/d=3.0
Figure 5. Instantaneous streamlines and vertical
vorticity contours in three sections as predicted by
DES.
(a) z/d=1.0
(b) z/d=2.0
(c) z/d=3.0
Figure 6. Instantaneous streamlines and vertical
vorticity contours in three sections as predicted by
RSM.
(a) DES
(b) RSM
Figure 8. Power spectra of the streamwise
drag coefficient
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