wind loading on curved circular cylinder structures
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Wind Load of a Curved Circular CylinderStructures
Conference Paper · October 2014
DOI: 10.13140/2.1.4758.1129
READS
138
2 authors:
Piotr Mieczysław Szczepaniak
Silesian University of Technology
18 PUBLICATIONS 9 CITATIONS
SEE PROFILE
Agnieszka Padewska
Silesian University of Technology
9 PUBLICATIONS 0 CITATIONS
SEE PROFILE
Available from: Piotr Mieczysław Szczepaniak
Retrieved on: 29 April 2016
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Proceedings of the 12th International Conference on
New Trends in Statics and Dynamics of BuildingsOctober 16-17, 2014 Bratislava, Slovakia
Faculty of Civil Engineering STU BratislavaSlovak Society of Mechanics SAS
WIND LOAD OF A CURVED CIRCULAR CYLINDER
STRUCTURES
P. Szczepaniak 1 and A. Padewska
2
Abstract
The paper presents the way of estimating the wind force acting on straight or curved elements with circularcross-section. These elements can be positioned at any angle to the wind direction. They may also be bent into
the form of a torus or a helix, laid horizontally or sloped. The first part of the work shows the analytical
approach to the problem, solved by decomposing the wind velocity vector to the normal, binormal and tangent
components, estimating the pressure distribution around the elements cross-section and finally integration of the
pressure over the whole surface. The second part of the article briefly presents the results of the air flow
computer simulations. Because there were observed significant differences between the data obtained from theanalytical and numerical method, some empirical correction functions had to be attached to the analytical
equations. The last part consists of the engineering applicable advices, presented on diagrams and tables of
coefficients.
Key Words
wind load; drag force; curved structure; numerical air flow computations
1 INTRODUCTION
Wind load is one of the most important load cases, acting on building structures. Procedures for calculating
the values of wind forces are precisely described in Eurocode 1 Part 1-4 [1]. However there is a specific, but
quite popular type of structure which is not covered by these standards. It means the building objects made
of various straight or curved circular cylinder elements, such as waterslides or other amusement ride devices
(Fig.1). For this type of structure the wind load is often the leading variable action, especially if the supports
have a static scheme of a vertical, fixed column with horizontal beams, where the bending moments
at the foundations level of the columns are the most important internal forces.The problems with calculations of the wind load are caused by the fact, that the longitudinal axis of these
structures is rarely perpendicular to the wind blows direction, as it is assumed in section 7.9 of [1]. So in
the current paper there is presented the way of estimating the value and direction of the wind force acting on
a straight cylinder, positioned at certain angle to the wind direction, and on a torus shaped structure, laid
horizontally or sloped.
1 PhD Eng. Piotr Szczepaniak, Silesian University of Technology, Faculty of Civil Engineering, Department of
the Theory of Building Structures, ul. Akademicka 5, 44-100 Gliwce, Poland, tel.: +48 608 524 333, e-mail:
piotr.szczepaniak@polsl.pl.2
MSc Eng. Agnieszka Padewska, Silesian University of Technology, Faculty of Civil Engineering, e-mail:agnieszkapadewska@gmail.com.
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Fig. 1. New waterslides at Gino Paradise Bešeňová, Slovakia
2 STANDARD PROCEDURE FOR CALCULATING WIND LOAD
In Eurocode 1 [1] the standard procedure for calculating the wind load acting on straight cylindrical elements
is described with the following basic formulas:
elements
ref e pf dsw )( A z qccc F (1)
where: F w – wind load force,cscd – structural factor, defined in section 6 of [1],
cf – force coefficient,
q p( z e) – peak velocity pressure at reference height z e (according to section 4.5 of [1]), Aref – reference area ( Aref = b l ),
b – diameter of the cylinder,
l – length of cylinder
0,f f cc (2)
cf,0 – force coefficient of cylinders without free-end flow,
ψ λ – end-effect factor (ψ λ ≤ 1)
)(2
)(e p
e
z qb
z vb Re
(3)
)10/log(4.01
)/10log(18.02.1105Re
60,f
5
Re
bk c
(4)
where: Re – Reynolds number,
k – equivalent surface roughness, given in Table 7.13 of [1],
v – wind speed,
υ – kinematic viscosity of the air ( /sm1015 26 ),
ρ – density of the air ( 3kg/m25.1 )
This procedure is sufficient if the structural element is distant from other ones and its axis is perpendicular to the
wind blows direction. In this case the main drag force has almost the same direction as the wind velocity vector,
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with its value slightly oscillating, which is caused by the von K ármán vortex shedding. In other cases, mainly
if the axis of the cylinder is positioned at different (not straight) angle to the wind blows, the drag force
is reduced, but at the same time appears a significant lift force, which is not taken under consideration in [1].
To cover this situation a more sophisticated procedure has to be developed.
3 GEOMETRY OF THE ELEMENT
At the first stage it is necessary to create a mathematical representation of the axis and surface of the element.
In most engineering structures made of cylindrical members its axes can be defined as a simple flat curve on
the Oxy plane, which is afterwards rotated and translated to the final position, as it is shown below.
T)();();()( z y x r r r r (5)
0 bRot )()( rrMr a (6)
where: r(α) – parametric vector equation of the axis in a Cartesian coordinate system,
r b(α) – base function,
MRot – rotation matrix,r0 – translation vector
)cos()sin(0
)sin()cos(0
001
)cos(0)sin(
010
)sin(0)cos(
100
0)cos()sin(
0)sin()cos(
Rot
x x
x x
y y
y y
z z
z z
M (7)
γ x , γ y , γ z – angles of sequential rotations around the axes of the coordinate system
Formulas for the most common base functions may be as follows:
Tline b, 0;0;)( r (8)
T
circle b, 0);sin();cos()( Rr (9)
T
helix b,2
);sin();cos()(
R Rr (10)
where: R – radius of the circle or helix,
δ – pitch of the helix
Having the parametric equation of the axis it is easy to calculate the unit long tangent (T1), normal (N1)
and binormal (B1) vectors, which create the Frennet-Serret basis of the local coordinate system.
3)('
)('')(')(
r
rr (11)
)('
)(')(11
r
rTT (12)
)('')('
)('')(')(0 11
rr
rrBB
(13)
vr
vrBB0vr
)('
)(')()('0 11
(14)
)()()( 1111 TBNN (15)
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sincos2
),(11 BNrS
b (16)
sincos,
1111 BNnn (17)
d d bb
dl b
d b
dA
)('cos
21
2cos
21
2r (18)
where: xxx – length (norm) of vector x,
κ – curvature of the axis,
v – wind velocity vector,
S(α,β ) – parametric equation of the surface of the element,
n1 – unit vector, normal to the surface
N
B
n1
d
dA
T
b
Fig. 2. Local TNB coordinate system
4 ANALYTICAL ESTIMATION OF THE WIND LOAD
4.1 Decomposition of the wind velocity vector and velocity pressure
The next step, after establishing the TNB local coordinate system, is decomposition of the wind velocity vector.
111111111e1e NNvBBvTTvvv z v z v (19)
11 N111B111T1 ;; NvBvTv vvv (20)
11N11B1T1e NBTv vvv z v (21)
where: v1 – unit long wind direction vector
Afterwards the velocity pressure has to be divided into the effects of longitudinal and perpendicular air flow.
BNT
2
N1
2
B1 p
2
T1 p
2
N1
2
B1
2
T1 p
2
N1
2
B1
2
T1
2
e11
2
e
2
222
)()(
qqvvqvqvvvq
vvv z v z v
q
vvv
v (22)
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4.2 Pressure distribution around the cross-section
The longitudinal air flow causes an uniform underpressure distribution around the cross-section of the element.
2
T1 pTT vqqq p (23)
Much more complicated is the pressure distribution resulting from the perpendicular air flow. It strongly depends
on the value of Reynolds number and the surface roughness, as it is presented on figure 7.27 in [1]. Similar
graphs, obtained from experiments in wind tunnel or numerical simulations, can be found in [3,4,5].Unfortunately there are no equations of the pressure distribution, and the only one applicable formula (25) has
been obtained from [2].
p0
2
N1
2
B1 p p0BNBN )( cvvqcqq p (24)
6cos03405cos12804cos0580
3cos50102cos6360cos32203560PN p0,
...
....c
(25)
,,arctan 1B1N0 vv (26)
where: c p0,PN – pressure distribution coefficient [2],
β 0 – angle of attack
Fig. 3. Air overpressure Δ p(qBN) distribution around the cross-section
The main drawback of the formula (25) is that the integration of the pressure distribution over the wholecircumference gives a constant value of the force coefficient (cf,PN). It is independent of the Reynolds number
and surface roughness, which is wrong according to equation (4). So there has been introduced a correction
factor (c p,cor ), that scales the values from equation (25) to produce the right force coefficient.
f,0
PN p0,
PNf, 5058.0
cos2
1
cconst b
d cb
c
(27)
cor p,PN p0, p0
f,0
PNf,
f,0
cor p,5058.0
cccc
c
cc (28)
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4.3 Distributed and resultant wind force
The next step after estimating the pressure is to calculate the wind force distribution along the element. It is done
by integration of the pressure distribution over the circumference of the cross-section.
w0ds
w0(BN)w0(T)
dsw0
dsw
w f FFFF
f ccd
d d ccd
d ccd
d
(29)
d
d d w0(BN)w0(T)
w0
FFf
(30)
d vqb
dAq pd
)('4
1
2
T1 p
2
1Tw0(T) rNnF (31)
d b
bbcvvq
dAccvvq
dAq pd
)('sin2sin4
9752.1
cos2cos9752.12112.24
)(
)(
100
100f,0
2
N1
2
B1 p
001 p0cor p,
2
N1
2
B1 p
001BNw0(BN)
rB
N
n
nF
(32)
The resultant wind force can be obtained by integration of the distributed wind load f w0 over parameter α.
2
1
w0w0
d f F (33)
w0dsw FF cc (34)
5 NUMERICAL AIR FLOW SIMULATIONS
Along with the analytical calculations, a large number of numerical air flow simulations were done. They were
made using the ANSYS software, especially the Fluent module. Computations were performed with the aid of
the PL-Grid Infrastructure.
5.1 Main parameters
First, there were modelled series of air flows past a straight cylinders with a diameter b = 1.0m, surfaceroughness k = 0.15mm, positioned at the angle against the wind direction (γ z ) in range from 30° to 90°,
at 15° steps. The computations were performed at the free flow speed ( v) equal to 11.0, 15.0, 22.0 and 33.5 m/s.It gives the Reynolds number in range from around 7.5·10
5 to 2.5·10
6, which indicates the supercritical type of
air flow, with a strong influence of the turbulent shear flow. To avoid the necessity of a very dense FVM mesh
near the cylinder surface, the k-ω/SST model has been chosen. The remaining boundary conditions are presentedon Fig. 4.
At the second stage there has been modelled the air flow past the half of a torus, with the same diameter, surface
roughness and wind speed as mentioned above. It has been positioned at slope angle (γ y) in range from 0° to 90°,
at 22.5° steps. The radius of curvature equals R = 3.0m – Fig. 5.
5.2 Results of the air flow simulations
Results of the numerical air flow simulations are presented in Tab. 1 and 2. There are also shown adequate
values obtained from the analytical calculations. It can be easily noticed, that as far as a straight cylinder is
concerned, the analytical underestimation of the wind force never exceeds 3 N/m, which is a completely
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insignificant value in civil engineering calculations. In most cases the wind force is slightly overestimated,
however the difference rarely exceeds 10%.
Much worse convergence of the results shows up in Tab. 2. However in the case of the not sloped torus ( γ y = 0)
the analytical results are acceptable, in other cases appears a significant underestimation of the y and z wind
force components. That’s why an empirical correction function has to be attached. Because it shouldn’t be anexplicit function of the main parameters, such as α and γ y angles, the following formulas are proposed:
12
2221
2
22
1
2
3
2
221
11
2
3
4
33
30,f p
2
w0
1.78.36.313.034.1cos702.1443.5363.4
65.2718.1143.44.388.1
5.287.009.943.3669.23
'2
N
N
B
rf
aaaaaa
aaaa
aaaa
acqb
(35)
where: )arccos( N11 va ,
)arcsin( B12 va ,
B13 va ,
w0
w0(BN)w0(T)
cor w0, f FF
f
d
d d (36)
These functions were obtained by finding a constant multipliers to B1 and N1 ( f B, f N) in successive ranges
of integration (αi, αi+1), which give a minimal difference of the wind force vector (37). Next these multipliers
were interpolated, using the arccos(v1N) as the independent variable. The improved analytical values are
presented in Tab. 3.
inumii
w
i
i
i
i
i
id f f d F ,
w01
)(
N1
)(
Bw00
11
1| FNBf
(37)
x
y
b
z
p=0
v x=v
v y=v
z =0
1m
f w0
num
x
z
v x=v
v x=v y=v z =0
v z =0
v z =0
b
p=0
Top view
Side view
v y=v
z =0
periodic b.c.
periodic b.c.
Fig. 4. Boundary conditions for the air flow simulations – straight cylinder
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x
y
p=0
v x=v
v y=v
z =0
v y=0
Fw0
num,i
x
z
v x=v v x=v y=v z =0
v z =0
v z =0
p=0
Top view
Side view
v y=v
z =0 b2 R
y
v y=0
i
i+1
Fw0
num,i
2 R
Fig. 5. Boundary conditions for the air flow simulations – half of a torus
Rotation
angle
γ z [°]
Numerical wind force
components
Analytical wind force
componentsnum
xw f ,0 [N/m] num
yw f ,0 [N/m]an
xw f ,0 [N/m]an
yw f ,0 [N/m]
v = 11 m/s; q p = 75.6 Pa; Re = 7.33·105; cf,0 = 0.663
30 8.0 -11.6 6.27 -10.85
45 18.8 -17.4 17.72 -17.72
60 33.4 -18.4 32.55 -18.80
75 45.5 -11.8 45.17 -12.10
90 48.4 0 50.12 0
v = 15 m/s; q p = 140.6 Pa; Re = 1.0·106; cf,0 = 0.692
30 14.2 -20.7 12.16 -21.06
45 34.5 -32 34.39 -34.39
60 60.6 -32.2 63.18 -36.48
75 82.4 -21.4 87.66 -23.49
90 94.2 0 97.27 0
v = 22 m/s; q p = 302.5 Pa; Re = 1.467·106; cf,0 = 0.72330 29.6 -42.7 27.35 -47.38
45 72.4 -67 77.37 -77.37
60 132.2 -73.1 142.13 -82.06
75 181.7 -47.2 197.21 -52.84
90 208.6 0 218.83 0
v = 33.5 m/s; q p = 701.4 Pa; Re = 2.23·106; cf,0 = 0.754
30 66.6 -95.8 66.10 -114.50
45 170.4 -158 186.97 -186.97
60 318.5 -175.6 343.49 -198.31
75 449.3 -116.7 476.59 -127.70
90 508.5 0 528.83 0
Tab. 1. Wind force components vs straight element rotation angle and wind speed
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Slope
angle
γ y [°]
Limits of
integrationNumerical wind force components Analytical wind force components
αi [°] αi+1 [°]inum
xw F ,
,0 [N]inum
yw F ,
,0 [N]inum
z w F ,
,0 [N]ian
xw F ,
,0 [N]ian
yw F ,
,0 [N]ian
z w F ,
,0 [N]
0
0 22.5 87.1 -16.5
0
102.07 -19.54
0
22.5 45.0 52.0 -33.3 53.49 -33.56
45.0 67.5 5.5 -1.9 4.51 -3.49
67.5 90.0 -2.5 37.4 -6.17 34.86
90.0 112.5 12.9 58.8 9.46 45.76
112.5 135.0 38.4 49.9 37.37 54.39
135.0 157.5 68.9 42.9 77.98 51.07
157.5 180.0 53.5 11.9 110.37 21.59
)(
0
i
w F 315.8 149.2 0 389.08 151.09 0
22.5
0 22.5 91.1 -13.9 24.4 103.85 -17.10 17.49
22.5 45.0 59.5 -27.4 37.2 62.31 -29.77 26.66
45.0 67.5 20.0 2.5 51.9 17.93 -4.25 30.91
67.5 90.0 11.0 48.6 18.3 3.33 31.12 21.96
90.0 112.5 19.1 64.4 10.8 15.78 49.10 11.20
112.5 135.0 39.4 42.4 26.4 44.18 57.36 4.10
135.0 157.5 83.9 22.8 38.6 82.12 51.19 -5.40
157.5 180.0 72.9 13.5 31.5 110.99 21.12 -13.61
)(
0
i
w F 396.9 152.9 239.1 440.48 158.78 93.32
45
0 22.5 98.6 -6.0 70.9 108.11 -10.44 31.03
22.5 45.0 79.3 -8.8 77.2 83.87 -17.97 43.35
45.0 67.5 55.7 6.9 71.9 54.89 -0.41 52.63
67.5 90.0 43.2 34.3 50.0 40.69 28.57 47.49
90.0 112.5 43.8 66.7 32.9 46.53 50.70 31.31
112.5 135.0 56.6 63.7 3.6 67.38 58.88 10.69135.0 157.5 66.8 30.3 -13.2 93.85 48.80 -10.70
157.5 180.0 50.0 8.8 -22.5 112.60 19.22 -25.45
)(
0
i
w F 494 195.9 270.8 607.92 177.35 180.35
67.5
0 22.5 110.0 12.3 78.1 112.39 -1.37 38.26
22.5 45.0 103.3 35.5 68.0 105.51 0.85 44.29
45.0 67.5 94.4 52.0 53.4 96.44 13.18 48.79
67.5 90.0 84.2 54.3 40.6 90.95 31.55 43.87
90.0 112.5 77.0 53.2 22.3 92.11 46.76 27.55
112.5 135.0 72.7 49.3 -6.7 99.09 50.65 3.90
135.0 157.5 70.0 35.1 -31.9 108.10 39.39 -19.54
157.5 180.0 66.4 12.6 -42.3 114.29 14.90 -34.25
)(
0i
w F 678 304.3 181.5 818.88 195.91 152.87
90
0 22.5 107.0 11.1 76.7 114.59 7.75 38.96
22.5 45.0 105.0 36.9 61.0 114.59 22.07 33.03
45.0 67.5 103.2 61.0 36.9 114.59 33.03 22.07
67.5 90.0 102.4 76.7 11.1 114.59 38.96 7.75
90.0 112.5 102.4 76.5 -11.0 114.59 38.96 -7.75
112.5 135.0 103.4 60.7 -36.0 114.59 33.03 -22.07
135.0 157.5 105.2 36.0 -60.7 114.59 22.07 -33.03
157.5 180.0 107.2 11.0 -76.5 114.59 7.75 -38.96
)(
0
i
w F 835.8 369.9 1.5 916.75 203.60 0.00
Tab. 2. Wind force components vs torus slope angle at v = 15m/s, R = 3.0m
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Slope
angle
γ y [°]
Limits of
integrationNumerical wind force components
Improved analytical wind force
components
αi [°] αi+1 [°]inum
xw F ,
,0 [N]inum
yw F ,
,0 [N]inum
z w F ,
,0 [N]ian
xw F ,
,0 [N]ian
yw F ,
,0 [N]ian
z w F ,
,0 [N]
0
0 22.5 87.1 -16.5
0
102.07 -19.54
0
22.5 45.0 52.0 -33.3 53.49 -33.56
45.0 67.5 5.5 -1.9 4.51 -3.49
67.5 90.0 -2.5 37.4 -6.17 34.86
90.0 112.5 12.9 58.8 9.46 45.76
112.5 135.0 38.4 49.9 37.37 54.39
135.0 157.5 68.9 42.9 77.98 51.07
157.5 180.0 53.5 11.9 110.37 21.59
)(
0
i
w F 315.8 149.2 0 389.08 151.09 0
22.5
0 22.5 91.1 -13.9 24.4 89.47 -14.16 25.57
22.5 45.0 59.5 -27.4 37.2 58.48 -25.85 33.59
45.0 67.5 20.0 2.5 51.9 16.40 4.34 41.21
67.5 90.0 11.0 48.6 18.3 5.04 50.19 35.52
90.0 112.5 19.1 64.4 10.8 24.59 63.34 26.50
112.5 135.0 39.4 42.4 26.4 47.00 50.12 26.49
135.0 157.5 83.9 22.8 38.6 66.10 33.15 29.12
157.5 180.0 72.9 13.5 31.5 83.81 12.97 28.76
)(
0
i
w F 396.9 152.9 239.1 390.89 174.10 246.77
45
0 22.5 98.6 -6.0 70.9 94.45 -1.78 81.04
22.5 45.0 79.3 -8.8 77.2 81.32 -2.01 76.38
45.0 67.5 55.7 6.9 71.9 60.77 8.44 67.59
67.5 90.0 43.2 34.3 50.0 44.35 37.14 53.25
90.0 112.5 43.8 66.7 32.9 46.98 63.32 28.34
112.5 135.0 56.6 63.7 3.6 59.31 57.99 4.83135.0 157.5 66.8 30.3 -13.2 66.07 34.56 -6.51
157.5 180.0 50.0 8.8 -22.5 69.54 11.46 -11.82
)(
0
i
w F 494 195.9 270.8 522.78 209.12 293.10
67.5
0 22.5 110.0 12.3 78.1 111.10 7.03 83.47
22.5 45.0 103.3 35.5 68.0 102.63 24.25 81.12
45.0 67.5 94.4 52.0 53.4 91.08 44.60 69.62
67.5 90.0 84.2 54.3 40.6 81.68 57.12 46.09
90.0 112.5 77.0 53.2 22.3 75.06 57.97 18.53
112.5 135.0 72.7 49.3 -6.7 72.10 53.48 -9.16
135.0 157.5 70.0 35.1 -31.9 73.08 40.15 -35.22
157.5 180.0 66.4 12.6 -42.3 74.72 15.01 -51.14
)(
0i
w F 678 304.3 181.5 681.44 299.62 203.30
90
0 22.5 107.0 11.1 76.7 113.49 14.30 71.91
22.5 45.0 105.0 36.9 61.0 113.49 40.74 60.97
45.0 67.5 103.2 61.0 36.9 113.49 60.97 40.74
67.5 90.0 102.4 76.7 11.1 113.49 71.91 14.31
90.0 112.5 102.4 76.5 -11.0 113.49 71.91 -14.31
112.5 135.0 103.4 60.7 -36.0 113.49 60.97 -40.74
135.0 157.5 105.2 36.0 -60.7 113.49 40.74 -60.97
157.5 180.0 107.2 11.0 -76.5 113.49 14.31 -71.91
)(
0
i
w F 835.8 369.9 1.5 907.90 375.84 0.00
Tab. 3. Improved wind force distribution
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6 CONCLUSIONS
For simplifying the manual calculations, the total effects of the axis curvature and rotation can be compressed
into a single vector coefficient μ, named position coefficient.
Tref 0,f pdsref 0,f pds
2
1
cor w0,dsw0dsw~;~;~~ z y x μ μ μ Acqcc Acqccd cccc μf FF
(38)
2
1
ref )('
d bl b A r (39)
2
1
0,f p
2
1
cor w0,
T
)('
~;~;~~
d bcq
d
μ μ μ z y x
r
f
μ (40)
)('
;;0,f p
cor w0,T
r
f μ
bcq z y x
(41)
where: μ x – longitudinal force position coefficient,
μ y – horizontal side force position coefficient,
μ z – vertical lift force position coefficient,
z y x ~,~,~ – averaged position coefficients
Distribution of this coefficient for sloped torus is presented on Fig. 6-8 and averaged values are also shown in
Tab. 4. All of these results were obtained using fixed values of the following parameters: wind direction
v1 = {1; 0; 0}T (wind blows along the x axis of the global coordinate system), rotation angles γ x = γ z = 0, relative
curvature ratio b·κ = 1/3.
For a straight cylinder the position coefficient has a constant value, given by equation (42).
222
2222
2/3222
T
straight
sincossinsincoscos
sincossinsincoscos
sincossin
;;
z y y y z y
z y y z z y
z y y
z y x
μ (42)
Fig. 6. Longitudinal force position coefficients μ x
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Fig. 7. Side force position coefficients μ y
Fig. 8. Lift force position coefficients μ z
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Slope
angle
γ y [°]
Limits of integration Averaged position coefficients
αi [°] αi+1 [°] x ~ [-] y
~ [-] z ~ [-]
0
0 22.5 0.891 -0.170
0
22.5 45.0 0.467 -0.293
45.0 67.5 0.039 -0.030
67.5 90.0 -0.054 0.304
90.0 112.5 0.083 0.399
112.5 135.0 0.326 0.475
135.0 157.5 0.680 0.446
157.5 180.0 0.963 0.188
22.5
0 22.5 0.781 -0.124 0.223
22.5 45.0 0.510 -0.226 0.293
45.0 67.5 0.143 0.038 0.360
67.5 90.0 0.044 0.438 0.310
90.0 112.5 0.215 0.553 0.231112.5 135.0 0.410 0.437 0.231
135.0 157.5 0.577 0.289 0.254
157.5 180.0 0.731 0.113 0.251
45
0 22.5 0.824 -0.016 0.707
22.5 45.0 0.710 -0.018 0.667
45.0 67.5 0.530 0.074 0.590
67.5 90.0 0.387 0.324 0.465
90.0 112.5 0.410 0.553 0.247
112.5 135.0 0.518 0.506 0.042
135.0 157.5 0.577 0.302 -0.057
157.5 180.0 0.607 0.100 -0.103
67.5
0 22.5 0.970 0.061 0.72822.5 45.0 0.896 0.212 0.708
45.0 67.5 0.795 0.389 0.607
67.5 90.0 0.713 0.498 0.402
90.0 112.5 0.655 0.506 0.162
112.5 135.0 0.629 0.467 -0.080
135.0 157.5 0.638 0.350 -0.307
157.5 180.0 0.652 0.131 -0.446
90
0 22.5 0.990 0.125 0.628
22.5 45.0 0.990 0.355 0.532
45.0 67.5 0.990 0.532 0.355
67.5 90.0 0.990 0.628 0.125
90.0 112.5 0.990 0.628 -0.125
112.5 135.0 0.990 0.532 -0.355135.0 157.5 0.990 0.355 -0.532
157.5 180.0 0.990 0.125 -0.628
Tab. 4. Averaged position coefficients
ACKNOWLEDGEMENT
This research has been partially supported by PL-Grid Infrastructure.
REFERENCES
[1] EN 1991-1-4:2005: Eurocode 1: Actions on structures - Part 1-4: General actions - Wind actions. CEN,
Brussels, 2005.
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[2] PN-B-02011:1977/Az1:2009: Obciążenia w obliczeniach statycznych. Obciążenie wiatrem (Loads in static
calculations. Wind loads). PKN, Warszawa 2009.
[3] Mallick M. – Kumar A.: Study on drag coefficient for the flow past a cylinder, International Journal of
Civil Engineering Research, Vol. 5, No. 4 (2014), pp. 301-306.
[4] Merrick R. – Bitsuamlak G.: Control of flow around a circular cylinder by the use of surface roughness:
A computational and experimental approach, Internet publication at http://www.ihrc.fiu.edu/wp-
content/uploads/2014/03/MerrickandBitsuamlak_FlowAroundCircularCylinders.pdf
[5] Lakehal D.: Computation of turbulent shear flows over rough-walled circular cylinders. Journal of Wind
Engineering and Industrial Aerodynamics, Vol. 80, Issues 1-2 (March 1999), pp. 47-68.
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