Antennas and open-frame structures Wind loading and structural response Lecture 23 Dr. J.D. Holmes Antennas and open-frame structures

Antennas and open-frame structures Antennas - isolated structures - radio telescopes and microwave antennas Antennas - attached to towers - aerodynamic interference Single frames Multiple frames Lattice towers 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 2f Paraboloid dish Normal to dish surface intersects axis at 2  focal length Approximate center of aerodynamic forces 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 boundary layer profile 0 20 40 60 80 90 Zenith angle, degrees 0.10 0.08 0.06 0.04 0.02 CM Zenith angle b Focus a Azimuth angle Wind Altitude axis PLAN VIEW

Antennas and open-frame structures Microwave dish antenna Impermeable dish 0.0 0.5 1.0 1.5 2.0 20 40 60 80 100 120 140 160 180 1% turbulence 10% turbulence  (degrees) b  A = (b2/4) (projected area) Small effect of turbulence

Antennas and open-frame structures Microwave dish antenna WIND Da Dt De Interference factor

Antennas and open-frame structures Microwave dish antenna Interference factor 0.5 1 1.5 45 90 135 180 Wind direction (degrees) Interference factor Experimental data Equation 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 120O Cd (ref.b)  0.8 b Cd 1.1

Antennas and open-frame structures 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

Antennas and open-frame structures Cell-phone antenna grouped panels 0o 60o total drag of group : about 30% less than sum of individual elements

Antennas and open-frame structures Single frame. Two-dimensional. Normal wind sharp-edged members 2.0 1.0 0.5 Solidity ratio,  CD solidity = ‘solid’ area of frame/total enclosed area reference area for drag coefficient = ‘solid’ area of frame drag coefficient relatively independent of details of member arrangement

Antennas and open-frame structures Single frame. Two-dimensional. Normal wind 2.0 1.0 0.5 Solidity ratio,  CD at low solidity, members act as individual elements at high solidity, frame acts as a solid plate (Lecture 8) intermediate solidity : aerodynamic interference between members CD  1.6

Antennas and open-frame structures Pairs of frames. Two-dimensional. Normal wind s b CD(2) = CD(1) [ 1 + 2] 1 CD(1) is drag coefficient of upstream frame (downstream frame influences upstream frame) 2 CD(1) is drag coefficient of downstream frame approximately, 1  1, 0 <  < 0.5 For circular members, equivalent solidity to calculate 2 , e  1.2 1.75

Antennas and open-frame structures angle of attack,  spacing/width = 1.0 spacing/width = 0.1 15 75 3 frames in series. Solidity = 0.1 X() = force normal to frame A = projected area of one frame at 0o angle of attack

Antennas and open-frame structures angle of attack,  spacing/width = 1.0 spacing/width = 0.1 15 75 3 frames in series. Solidity = 0.5 A = projected area of one frame at 0o angle of attack Maximum CXN at 30o to 45o

Antennas and open-frame structures angle of attack,  spacing/width = 1.0 spacing/width = 0.1 15 75 10 frames in series. Solidity = 0.1 A = projected area of one frame at 0o angle of attack

Antennas and open-frame structures angle of attack,  spacing/width = 1.0 spacing/width = 0.1 15 75 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

Antennas and open-frame structures Design method : ‘Wind loads and anchor bolt design for petrochemical facilities’ (ASCE) Needs more wind tunnel studies for pipe racks etc.

Antennas and open-frame structures Drag coefficients for lattice tower (Lecture 21) Square cross section with flat-sided members (wind normal to face) Australian Standards 0.0 0.2 0.4 0.6 0.8 1.0 Solidity Ratio d 4.0 3.5 3.0 2.5 2.0 1.5 Drag coefficient CD (q=0O) CD = 4.2 - 7 (for 0.1< < 0.2) CD = 3.5 - 3.5 (for 0.2< < 0.5) (ASCE-7 : CD = 4.02 – 5.9 +4.0 )  = solidity of one face = area of members  total enclosed area includes interference and shielding effects between members

Antennas and open-frame structures Drag coefficients for lattice tower Triangular cross section with flat-sided members CD = 3.5 - 4 (for 0.1< < 0.3) CD = 2.9 – 2 (for 0.3<  < 0.5) (ASCE-7 : CD = 3.42 – 4.7 +3.4 )

Antennas and open-frame structures Drag coefficients for lattice tower Cross section with circular members depends on Reynolds Number for super-critical flow - Cd for cross section ~ 0.5 times that for equivalent sharp-edged tower with same solidity some members may be in super-critical flow - others in sub-critical flow

End of Lecture 23 John Holmes 225-405-3789 JHolmes@lsu.edu