03 Lect 23 Antennas

7/29/2019 03 Lect 23 Antennas

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Antennas and open-frame

structures

Wind loading and structural response

Lecture 23 Dr. J.D. Holmes


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Antennas and open-frame structures

Single frames

Multiple frames

Antennas - isolated structures - radio telescopes and microwave

antennas

Lattice towers

Antennas - attached to towers - aerodynamic interference

Common feature : aerodynamic interference between various elements - e.g.

antennas and supporting tower or other antennas, members of a frame


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Radio telescope

Paraboloid dish

f

Focus


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Radio telescope

Paraboloid dish

Normal to dish surface intersects axis at 2 focal length

2f

Approximate center of aerodynamic forces2

2fed

e

d

C


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Radio telescope

Paraboloid dish

Wind

FX

FY

e

b

d

Fy force generates significant moments about dish supports


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Radio telescope

Paraboloid dish

Total

moment

Azimuth

angle,

135o

Altitude

moment

Azimuth

moment

Effect of

boundary

layer

profile

0 20 40 60 80 90

Zenith angle, degrees

0.10

0.08

0.06

0.04

0.02

0

CM

Zenith

angle b

Focus

aAzimuth

angle

WindAltitude

axis

PLAN VIEW

AbU

MC

2

ha21M


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Microwave dish antenna

Impermeable dish

Small effect of turbulence

0.0

0.5

1.0

1.5

2.0

0 20 40 60 80 100 120 140 160 180

1% turbulence

10% turbulence

(degrees)

b

A2

a2

1D

U

)D()(C

A = (b2/4)

(projected area)


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Interference factor WIND

WIND

Da

WINDDt

De

aD

tD

eD

iK

a.Di

Kt

De

D


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Interference factor

0

0.5

1

1.5

0 45 90 135 180Wind direction (degrees)

Interference

factor

Experimental data

Equation with t=0.5

Ki = exp [-k(CD )2]. [(1+t) + t cos 2( - d - 90)]


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Cell-phone antenna

isolated panels

b

Cd1.1

120O

Cd (ref.b) 0.8


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Cell-phone antenna

grouped panels

~2b

combined

Cd (ref.b) 1.1

combined

Cd (ref.b) 0.9

grouping gives large reduction in total drag


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Cell-phone antenna

grouped panels

total drag of group : about 30% less than sum of individual elements

0o

60o


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Open frames Single frame. Two-dimensional. Normal wind sharp-edged members

reference area for drag coefficient = solid area of frame

2.0

1.0

0.5 1.00Solidity ratio,

CD

solidity = solid area of frame/total enclosed area

drag coefficient relatively independent of details of member arrangement


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Open frames Single frame. Two-dimensional. Normal wind

at high solidity, frame acts as a solid plate (Lecture 8)

at low solidity, members act as individual elements

intermediate solidity : aerodynamic interference between members CD 1.6

2.0

1.0

0.5 1.00Solidity ratio,

CD


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Open frames Pairs of frames. Two-dimensional. Normal wind

1 CD(1) is drag coefficient of upstream frame

(downstream frame influences upstream frame)

CD(2) = CD

(1) [ 1 + 2]

2 CD(1) is drag coefficient of downstream frame

approximately, 1 1,

0.45

0.45

2b

s1

sb

For circular members, equivalent solidity to calculate 2,

e 1.2 1.75

0 < < 0.5


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Open frames

3 frames in series. Solidity = 0.1

X(a) = force normal to frame

AU

)X()(C

2a2

1

N

X

angle of attack, a

spacing/width = 1.0

spacing/width = 0.1

15 75

A = projected area of one frame at

0o angle of attack


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Open frames


A = projected area of one frame at0o angle of attack

Maximum CXN at 30o to 45o

angle of attack, a

spacing/width = 1.0

spacing/width = 0.1

15 75

AU

)X()(C2

a21

N

X


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Open frames



angle of attack, a

spacing/width = 1.0

spacing/width = 0.1

15 75

AU)X()(C2

a21

NX


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Open frames



Maximum CXN at 30o to 45o

angle of attack, a

spacing/width = 1.0

spacing/width = 0.1

15 75

AU)X()(C2

a21

NX



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Open frames

Design method :

Wind loads and anchor bolt design for petrochemical facilities (ASCE)

Needs more wind tunnel studies for pipe racks etc.


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Drag coefficients for lattice tower (Lecture 21)

= solidity of one face = area of members total enclosed area

AustralianStandards

0.0 0.2 0.4 0.6 0.8 1.0Solidity Ratio

4.0

3.5

3.0

2.5

2.0

1.5

Drag

coefficient

CD (=0O)

Square cross section with flat-sided members (wind normal to face)

(ASCE-7 : CD = 4.025.9 +4.0 )

includes interference and shielding effects between members


CD = 4.2 - 7 (for 0.1


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Drag coefficients for lattice tower

CD = 3.5 - 4 (for 0.1


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Drag coefficients for lattice tower

depends on Reynolds Number

for super-critical flow - Cd for cross section ~ 0.5 times that for

equivalent sharp-edged tower with same solidity

Cross section with circular members


some members may be in super-critical flow - others in sub-critical flow


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End of Lecture 23

John Holmes225-405-3789 [email protected]

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03 Lect 23 Antennas