Antennas and open- frame structures Wind loading and structural response Lecture 23 Dr. J.D. Holmes
Dec 22, 2015
Antennas and open-frame structures
Wind loading and structural response
Lecture 23 Dr. J.D. Holmes
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
Antennas and open-frame structures
• Radio telescope
• Paraboloid dish
f
Focus
Antennas and open-frame structures
• Radio telescope
• Paraboloid dish
Normal to dish surface intersects axis at 2 focal length
2f
Approximate center of aerodynamic forces2
2fed
e
d
C
Antennas and open-frame structures
• Radio telescope
• Paraboloid dish
Wind
FX
FY
e
b
d
Fy force generates significant moments about dish supports
Antennas and open-frame structures
• Radio telescope
• Paraboloid dish
Total moment
Azimuth angle, 135o
Altitude moment
Azimuth moment
Effect of boundarylayer profile
0 20 40 60 80 90Zenith angle, degrees
0.10
0.08
0.06
0.04
0.02
0
CM
Zenith angle
Focus
Azimuth
angle
Wind
Alti
tude
ax
is
PLAN VIEW
AbUρ
MC 2
ha21M
Antennas and open-frame structures
• 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)
bA2
a21D Uρ
)D()(C
A = (b2/4) (projected area)
Antennas and open-frame structures
• Microwave dish antenna
• Interference factor WIND
WIND
Da
WINDDt
De
aDtDeD
iK
a.DiKtDeD
Antennas and open-frame structures
• Microwave dish antenna
• Interference factor
0
0.5
1
1.5
0 45 90 135 180Wind direction (degrees)
Inte
rfe
renc
e fa
ctor
Experimental dataEquation with t=0.5
Ki = exp [-k(CD)2]. [(1+t) + t cos 2( - d - 90)]
Antennas and open-frame structures
• Cell-phone antenna
• isolated panels
b
Cd 1.1
120O
Cd (ref.b) 0.8
Antennas and open-frame structures
• Cell-phone antenna
• grouped panels
~2b
combinedCd (ref.b) 1.1
combinedCd (ref.b) 0.9
grouping gives large reduction in total drag
Antennas and open-frame structures
• Cell-phone antenna
• grouped panels
total drag of group : about 30% less than sum of individual elements
0o
60o
Antennas and open-frame structures
• 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 1.00
Solidity ratio,
CD
solidity = ‘solid’ area of frame/total enclosed area
drag coefficient relatively independent of details of member arrangement
Antennas and open-frame structures
• 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 1.00
Solidity ratio,
CD
Antennas and open-frame structures
• 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,
0.45δ0.45
2 b
sδ1ψ
sb
For circular members, equivalent solidity to calculate 2 , e 1.2 1.75
0 < < 0.5
Antennas and open-frame structures
• Open frames
• 3 frames in series. Solidity = 0.1
X() = force normal to frame
AUρ
)X()(C
2a2
1
NX
αα
angle of attack,
spacing/width = 1.0
spacing/width = 0.1
15 75
A = projected area of one frame at 0o angle of attack
Antennas and open-frame structures
• Open frames
• 3 frames in series. Solidity = 0.5
A = projected area of one frame at 0o angle of attack
Maximum CXN at 30o to 45o
angle of attack,
spacing/width = 1.0
spacing/width = 0.1
15 75
AUρ
)X()(C
2a2
1
NX
αα
Antennas and open-frame structures
• Open frames
• 10 frames in series. Solidity = 0.1
A = projected area of one frame at 0o angle of attack
angle of attack,
spacing/width = 1.0
spacing/width = 0.1
15 75
AUρ
)X()(C
2a2
1
NX
αα
• Open frames
• 10 frames in series. Solidity = 0.5
A = projected area of one frame at 0o angle of attack
Maximum CXN at 30o to 45o
angle of attack,
spacing/width = 1.0
spacing/width = 0.1
15 75
AUρ
)X()(C
2a2
1
NX
αα
Antennas and open-frame structures
Antennas and open-frame structures
• Open frames
• Design method :
‘Wind loads and anchor bolt design for petrochemical facilities’ (ASCE)
Needs more wind tunnel studies for pipe racks etc.
• Drag coefficients for lattice tower (Lecture 21)
= solidity of one face = area of members total enclosed area
Australian Standards
0.0 0.2 0.4 0.6 0.8 1.0
Solidity Ratio
4.0
3.5
3.0
2.5
2.0
1.5
Dra
g co
effic
ient
C
D (
=0O
)
Square cross section with flat-sided members (wind normal to face)
(ASCE-7 : CD = 4.02 – 5.9 +4.0 )
includes interference and shielding effects between members
Antennas and open-frame structures
CD = 4.2 - 7 (for 0.1< < 0.2)
CD = 3.5 - 3.5 (for 0.2< < 0.5)
• Drag coefficients for lattice tower
CD = 3.5 - 4 (for 0.1< < 0.3)
CD = 2.9 – 2 (for 0.3< < 0.5)
Triangular cross section with flat-sided members
(ASCE-7 : CD = 3.42 – 4.7 +3.4 )
Antennas and open-frame structures
• 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
Antennas and open-frame structures
some members may be in super-critical flow - others in sub-critical flow
End of Lecture 23
John Holmes225-405-3789 [email protected]