CHEMICAL ENGINEERING TRANSACTIONS
VOL. 76, 2019
A publication of
The Italian Association
of Chemical Engineering
Online at www.aidic.it/cet
Guest Editors: Petar S. Varbanov, Timothy G. Walmsley, Jiří J. Klemeš, Panos Seferlis
Copyright © 2019, AIDIC Servizi S.r.l.
ISBN 978-88-95608-73-0; ISSN 2283-9216
Computational Method Study on Drag Coefficient of Butterfly
Porous Fence
Zhenya Duana, Zhujun Lana, Jin Sud, Kai Wanga, Chi Zhoua,b, Junmei Zhangc,*
aElectromechanical Engineering College, Qingdao University of Science and Technology, Qingdao, China
bShanghai Turing Info Technology Co., Ltd, Shanghai, China
cCollege of Chemical Engineering, Qingdao University of Science and Technology, Qingdao, China
dQingdao Changlong Power Equipment Co., Ltd, Qingdao, China
qust_zyduan@163.com
To study the drag coefficient of butterfly porous fence, this study proposes the computational model of butterfly
porous fence based on the wind tunnel experiment. Effects of wind speed, porosity and hole diameter on the
drag coefficient of the butterfly porous fence are investigated through the ANSYS Fluent. Under different wind
speeds, the measurement results of the flow field behind the porous fence by the micro-particle image
velocimetry (PIV) technology are found to be in good agreement with the numerical simulation. The numerical
model can be considered correct and the simulation method is reasonable. Through the analysis of the
simulation, research groups obtained some conclusions. Wind speed has almost no effect on drag coefficient
when the maximum wind speed is over 10.0 m/s. The drag coefficient of the butterfly porous fence decreases
gradually with the increase of porosity. Based on the simulation, the formula is established among drag
coefficient, porosity and hole diameter when d is 6.6 mm ~ 9.5 mm. The research provides some theoretical
basis for the butterfly porous fence engineering design. At the same time, it can effectively suppress dust
diffusion to lighten the pollution of air.
1. Introduction
It was easy to produce dust pollution in open coal yards. These dusts could cause serious air pollution (Duan et
al., 2017). Xu et al. (2010) had determined the drag coefficient of porous fence. He studied the drag coefficient
of butterfly porous fence by means of pressure measurement and force measurement, which obtained the linear
expression of the drag coefficient of the porous fence under different aperture. Chen et al. (2015) used CFD (
computational fluid dynamics) to carry out numerical simulation research on diversion porous fence. Under
certain conditions, the difference of wind load was small between two kinds of porous fence. Wind load increases
quadratically with the wind speed.
By analyzing drag coefficients, research groups could quantitatively study the force of the porous fence.
Briassoulis et al. (2010) used the elevated plate as the research object. He carried out numerical simulation and
actual measurement on the drag coefficient of the elevated plate. The results showed that the drag coefficient
could be an effective measure on the aerodynamic behavior of the open stencil.
Zhou (2017) studied on the drag coefficient of flat porous fence. Formula for the drag coefficient of the porous
fence were summarized. According to the research of Xu et al. (2017), a butterfly porous fence model was
established. ANSYS Fluent (Han, 2009) and wind tunnel experiment were used to study the drag coefficient of
a butterfly porous fence (Ferreira et al., 2011).
Wind load should be considered in the design of butterfly porous fence. It was related to drag coefficient, but
there were few theoretical studies at present, which restricts the popularization of butterfly porous fence.
Research groups introduce butterfly porous fence model and numerical simulation. Then, results of PIV and
numerical simulation were compared. Finally, results and discussion were obtained in this paper. The formula
for the drag coefficient of a butterfly porous fence were summarized. The research provided some theoretical
basis for the butterfly porous fence engineering design. At the same time, it can effectively suppress dust
diffusion, to lighten the pollution of air.
DOI: 10.3303/CET1976015
Paper Received: 07/03/2019; Revised: 30/04/2019; Accepted: 06/05/2019
Please cite this article as: Duan Z., Lan Z., Su J., Wang K., Zhou C., Zhang J., 2019, Computational Method Study on Drag Coefficient of
Butterfly Porous Fence, Chemical Engineering Transactions, 76, 85-90 DOI:10.3303/CET1976015
85
2. Butterfly porous fence model and numerical simulation
2.1 Butterfly porous fence model
The structure of butterfly porous fence model was shown in Figure 1. Butterfly porous fence had the porosity of
0.270, the length of 600 mm, the width of 125 mm, the thickness of 1 mm, and the hole of 6 mm.
Figure 1: Schematic diagram of butterfly porous
fence
Figure 2: Computational model
Model was established by SOLIDWORKS. Length of the model was 2,600 mm (20.8 H), and size of the cross
section was 600 mm (4.8 H) × 600 mm (4.8 H). Butterfly porous fence was placed 600 mm (4.8 H) away from
the entrance of the calculation model. The height H (125 mm) of butterfly porous fence was used as the
reference for 3D model. It was shown in Figure 2.
2.2 Governing equation
In the ANSYS Fluent, wind was regarded as incompressible fluid, which abides by the conservation of mass,
momentum, dissipation rate equation and turbulent flow additional turbulent kinetic energy equation.
2.2.1 Mass conservation equation
0
u
x y z
+ + =
(1)
Where u was the velocity in the x direction, was the velocity in the y direction, and was the velocity in
the z direction.
2.2.2 Momentum conservation equation
2
2
3
ji i i
j ij
j j j j i i
uu u uk p
u C k
x x x x x x
= + + − −
(2)
Where ρ was density of gas kg/m3, ui was the velocity component in the i direction m/s, uj was the velocity
component in the j direction m/s, xi was coordinates in the X direction, xj was coordinates in the Y direction, δij
was Kronecker tensor, and μ was aerodynamic viscosity coefficient kg/(m·s).
2.2.3 Governing equations for turbulence simulation
Research groups were referred to Giannoulis et al. (2010). The RNG k-ε equation used in the simulation was
obtained from Hong et al. (2015). Eq(3) in the presented study is equation k in the original study, and Eq(4) is
equation ε.
( )i
eff
i j j
ku k
G
x x x
= + −
(3)
( ) 2
1
2
i
eff
i j j
u C
G C
x x x
= + −
(4)
ji i
t
j j i
uu u
G
x x x
= +
(5)
86
eff t
= + ,
2
t
C
= ,
( )0
1 1 3
1 /
1
C C
−
= −
+
, ( )
1/ 2
2
ij ij
E E
= • ,
1
2
ji
ij
j i
uu
E
x x
= +
.
Where Cμ(0.0845) was selected by experience, Gk was production term of turbulent kinetic energy k (caused by
average velocity gradient), αk (1.39) was Prandtl number corresponding to kinetic energy k, αε (1.39) was Prandtl
number corresponding to the dissipation rate ε, μt was turbulence viscosity coefficient kg/(m·s), η0 = 4.377 β =
0.012 was coefficient of thermal expansion K-1, C1ε was turbulence factor, the value was 1.42, C2ε was turbulence
factor, the value was 1.68, and Eij was average rate of change per hour.
2.3 Independence of grid
The number of grids includes: 2,968,686, 3,629,952, 4,847,386, 5,618,815 and 6,139,707. Overall force of the
stencil as the grid independence verification index was taken. Overall force of the butterfly porous fence
decreases with the increase of the number of grids. The difference of the butterfly porous fence overall force
was only 0.11 between the grids number of 5,618,815 and the grids number of 6,139,707. The number of
computational grids was determined to be 5,618,815 without affecting the simulation.
2.4 Simulation condition setting
The simulation chose pressure-based discrete solution method in the solver. The calculation accuracy was set
to 10-5, the solution method adopted SIMPLEC algorithm, and the calculation method was steady calculation.
The boundary conditions were shown in Table 1.
Table 1: Boundary conditions
Boundary condition type Setting conditions
Entrance boundary condition Speed entry, exponential function
Export boundary conditions Free flow, full development
Top side, two sides Zero shear slip wall
3. Results of PIV experiment and numerical simulation
The butterfly porous fence with the porosity of 0.270 had the wind velocity of 4.0 m/s and 10.0 m/s. A distribution
diagram of the net flow line was obtained by numerical simulation and PIV experiment in Figure 3. In the Figure
3, the position of the butterfly porous fence was X = 0 mm. X = 100 mm was 100 mm behind the butterfly porous
fence. Y = 40 mm meant that the fence height of the butterfly porous fence was 40 mm.
In the Figure 3, the first picture was a numerical simulation of wind speed of 4.0 m/s. The second picture was a
PIV of wind speed of 4.0 m/s. The next picture was a numerical simulation of wind speed of 10.0 m/s. The last
picture was a PIV of wind speed of 10.0 m/s. Velocity distribution of the numerical simulation was the same as
the velocity distribution of the PIV in Figure 3. The streamline distribution was basically the same in the trend.
The wind speed in the top area of the butterfly porous fence was higher than that in the rest area. Therefore,
there was a high wind speed area. The section of the butterfly porous fence was uneven. There was low wind
speed area with vortex shedding. It was accompanied by some vortices near the fence height of the butterfly
porous fence after the wind passed through the butterfly porous fence. Due to the accumulation of tracer
particles during wind tunnel experiments, measurement errors may be occurred in PIV. The numerical simulation
was different from the PIV far away from the butterfly porous fence.
In order to analyze the difference of numerical simulation and PIV, the value of the velocity distribution in the X
direction of the fence height (Y = 125 mm) section were plotted as Figure 4.
(a) Wind speed 4.0 m/s (b) Wind speed 10.0 m/s
Figure 3: Comparison of the streamlines between numerical simulation and PIV after butterfly porous fence at
(a) 4.0 m/s (b) 10.0 m/s
87
-20 0 20 40 60 80 100 120 140 160 180 200 220
-4
-2
0
2
4
6
8
S
p
e
e
d
i
n
t
h
e
X
d
ir
e
c
ti
o
n
/m
/s
Backplane distance/mm
10m/s-CFD
10m/s-PIV
Y=125mm
-20 0 20 40 60 80 100 120 140 160 180 200 220
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
S
p
e
e
d
i
n
t
h
e
X
d
ir
e
c
ti
o
n
/m
/s
Backplane distance/mm
4m/s-CFD
4m/s-PIV
Y=125mm
(a)Wind speed 4.0 m/s (b) Wind speed 10.0 m/s
Figure 4: Comparison results of numerical simulation and PIV in the Y = 125 mm for wind speed at (a) 4.0 m/s
(b) 10.0 m/s
The simulated value of the speed in the X direction on the section of the fence height (Y = 125 mm) was the
same as the experimental value in Figure 4. Under the same speed of wind, the numerical simulation of the
same position behind the fence was close to the PIV. Their relative error was within 15 %, the minimum relative
error was only 1 %, and the average relative error was 20 %. There were some vortices after the wind passed
through the butterfly porous fence. In the numerical simulation and the PIV, the X direction velocity of the
butterfly porous fence had a negative value. With the increase of distance, the speed in the X direction was from
negative to positive. The results of the numerical simulation agreed well with the results of the PIV within the
allowable range of error.
4. Results and discussion
4.1 Drag coefficient calculation formula
And worldwide, the wind load calculation formula for porous fence was (6)：
21
2
d ref ref
F c A = (6)
This paper defined the drag coefficient by referring to formula (6):
2
/
2 n
ref
d
F A
c
= (7)
Where F was the force N, Aref was the porous fence area on the outer contour m2, An was the porous fence
projection area in downwind direction m2, ρ was the gas density kg/m3,
ref
was the wind speed at reference
height m/s, and cd was the drag coefficient.
4.2 Effects of wind speed（
ref
）on the drag coefficient（cd）
Groups chose the butterfly porous fence whose porosity was 0.270 and hole diameter was 6 mm. the values of
the wind speed were 3.0 m/s, 5.0 m/s, 7.0 m/s, 10.0 m/s, 12.0 m/s, 15.0 m/s, 18.0 m/s and 22.0 m/s.
0 2 4 6 8 10 12 14 16 18 20 22 24
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
D
r
a
g
c
o
e
ff
ic
ie
n
t
Wind speed / m/s
Opening rate0.270
0.10 0.15 0.20 0.25 0.30 0.35 0.40
2.00
2.05
2.10
2.15
2.20
2.25
D
r
a
g
c
o
e
ff
ic
ie
n
Opening rate
Wind speed10 m/s
Figure 5: Curves of drag coefficient varying with
wind speed
Figure 6: Curves of drag coefficient varying with
different open porosity
88
The drag coefficient of the butterfly porous fence decreases with the increase of wind speed in Figure 5. It was
almost unaffected by the change of wind speed. Under the condition of different porosity, the difference value
was 0.03 between the maximum drag coefficient and the minimum drag coefficient. The change rate of drag
coefficient was only 1.4 %. According to Load code for the design of building structures from the statistics of
wind loads in different regions, when the maximum wind speed was over 10.0 m/s, the drag coefficient basically
did not change. The drag coefficient of the butterfly porous fence was almost not affected by the change of
wind speed.
4.3 Effects of porosity（ ）on the drag coefficient（cd）
In the Figure 6, research groups chose the butterfly porous fence whose hole diameter was 6 mm. It depicted
that drag coefficient changed with porosity when the wind speed was 10.0 m/s.
The porosity can be obtained by changing the lateral spacing between the butterfly porous mesh. In order to
study the effect of the porosity on the drag coefficient, Butterfly porous fences were designed whose porosity
were 0.134, 0.222, 0.270, 0.318 and 0.358. The drag coefficient of the butterfly porous fence was affected by
the porosity, and the drag coefficient of the butterfly porous fence decreases gradually with the increase of
porosity in Figure 6.
4.4 Drag coefficient formula fitting of the butterfly porous fence
When porosity was 0 ~ 0.367 at different hole diameters, the followings were the fitting formula for the numerical
simulation of the butterfly porous fence drag coefficient:
(1) When the hole diameter was 6.6 mm: (Correlation coefficient: R2 = 0.996)
0.448 2.280
d
c = − + (8)
(2) When the hole diameter was 7.4 mm: (Correlation coefficient: R2 = 0.991)
0.624 2.283
d
c = − + (9)
(3) When the hole diameter was 8.1 mm: (Correlation coefficient: R2 = 0.996)
0.702 2.281
d
c = − + (10)
(4) When the hole diameter was 8.6 mm: (Correlation coefficient: R2 = 0.998)
0.768 2.282
d
c = − + (11)
(5) When the hole diameter was 9.5 mm: (Correlation coefficient: R2 = 0.997)
0.870 2.274
d
c = − + (12)
By analyzing the formula (8) ~ (12), it can be summarized as a general type.
2.280
d
c k= + (13)
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
1.90
1.95
2.00
2.05
2.10
2.15
2.20
2.25
2.30
2.35
D
r
a
g
c
o
e
ff
ic
ie
n
Opening rate
Hole diameter is 6.6mm
Hole diameter is 7.4mm
Hole diameter is 8.1mm
Hole diameter is 8.6mm
Hole diameter is 9.5mm
0 1 2 3 4 5 6 7 8 9 10
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
E
q
u
a
ti
o
n
s
lo
p
e
Hole diameter/mm
Figure 7: Changing curve of butterfly porous fence
of drag coefficient at different hole diameters
Figure 8: Changing curve slope of fitting equation
at different hole diameters
In Eq(13), k was the slope of the fitted equation. It could be attributed to the function of the hole diameter.
89
( )k f d= (14)
In the Figure 8, the relationship between the slope of the fitted equation and the hole diameter was nonlinear.
As the hole diameter increases, the slope of the fitted equation became smaller than before.
When d was 6.6 mm ~ 9.5 mm. (Correlation coefficient: R2 = 0.986)
2
0.00185 0.030 0.0067k d d= − − (15)
5. Conclusion
This paper aims to study the drag coefficient of butterfly porous fence. The PIV technique is used to compare
the PIV of the butterfly porous fence with the numerical simulation. It verified the correction of the numerical
simulation and draws the following conclusions：
(1) When the wind load is calculated, the wind speed usually exceeds 10.0 m/s. There was almost no influence
on the drag coefficient of the butterfly porous fence.
(2) Cd and k are different for different hole diameters in this paper. When d is 6.6 mm ~ 9.5 mm, k = 0.00185-
0.030 × d-0.0067 × d2.
The correctness of the numerical model are verified through experiments, but the correctness of the formula are
not verified with experiments. Consequently, the proposed formula has certain limitations. Future works need to
be done to expand the scope of the application of the formula. A critical step is to investigate the features of the
porosity and the hole diameter to obtain a more general formula.
Acknowledgments
This paper has been supported by the science and technology of people's livelihood fund project in Qingdao
(Research Project: 15-9-2-113-nsh). The national environmental protection atmospheric combined pollution
source and control key laboratory open fund project (Research Project: SCAPC201405). The natural science
fund project of Shandong Provincial (Research Project: ZR2015DL007).
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