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

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Piotr Mieczysław Szczepaniak

Silesian University of Technology

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Agnieszka Padewska

Silesian University of Technology

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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:

[email protected]

MSc Eng. Agnieszka Padewska, Silesian University of Technology, Faculty of Civil Engineering, e-mail:[email protected].



12th International Conference on New Trends in Statics and Dynamics of Buildings October 2014, Bratislava

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,




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)




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)




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)




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




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




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




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




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




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




Fig. 7. Side force position coefficients μ y

Fig. 8. Lift force position coefficients μ z




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.




[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.

wind loading on curved circular cylinder structures

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