Antennas and open-frame structures

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

2. 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

3. f Focus Antennas and open-frame structures • Radio telescope • Paraboloid dish

4. 2f Approximate center of aerodynamic forces d C e Antennas and open-frame structures • Radio telescope • Paraboloid dish Normal to dish surface intersects axis at 2  focal length

5. FY d FX e  b Wind Antennas and open-frame structures • Radio telescope • Paraboloid dish Fy force generates significant moments about dish supports

6. Focus 0.10 0.08 0.06 0.04 0.02 0 Total moment Azimuth angle, 135o Effect of boundary layer profile Zenith angle b Altitude moment CM Azimuth moment Wind Altitude axis Azimuth angle 0 20 40 60 80 90 Zenith angle, degrees a PLAN VIEW Antennas and open-frame structures • Radio telescope • Paraboloid dish

7. 2.0 1.5 b  1.0 0.5 1% turbulence 10% turbulence 0.0 120 140 160 0 40 60 180 80 100 20  (degrees) Antennas and open-frame structures • Microwave dish antenna • Impermeable dish A = (b2/4) (projected area) Small effect of turbulence

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

9.  Experimental data Equation with t=0.5 1.5 1 Interference factor 0.5 0 0 45 90 135 180 Wind direction (degrees) Antennas and open-frame structures • Microwave dish antenna • Interference factor Ki = exp [-k(CD)2]. [(1+t) + t cos 2( - d - 90)]

10. Cd (ref.b)  0.8 Cd1.1 120O b Antennas and open-frame structures • Cell-phone antenna • isolated panels

11. combined Cd (ref.b)  1.1 combined Cd (ref.b)  0.9 ~2b Antennas and open-frame structures • Cell-phone antenna • grouped panels grouping gives large reduction in total drag

12. 60o 0o Antennas and open-frame structures • Cell-phone antenna • grouped panels total drag of group : about 30% less than sum of individual elements

13. 2.0 CD 1.0 0 0.5 1.0 Solidity ratio, Antennas and open-frame structures • Open frames • Single frame. Two-dimensional. Normal wind • sharp-edged members 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

14. 2.0 CD 1.0 0 0.5 1.0 Solidity ratio,  Antennas and open-frame structures • Open frames • Single frame. Two-dimensional. Normal wind 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

15. b s approximately, 1  1, Antennas and open-frame structures • Open frames • Pairs of frames. Two-dimensional. Normal wind 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 0 <  < 0.5 For circular members, equivalent solidity to calculate 2 , e  1.2 1.75

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

17. spacing/width = 1.0 spacing/width = 0.1 15 75 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

18. spacing/width = 1.0 spacing/width = 0.1 15 75 angle of attack,  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

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

20. 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.

21. 4.0 3.5 3.0 2.5 2.0 1.5 Drag coefficient CD (q=0O) Australian Standards 0.0 0.2 0.4 0.6 0.8 1.0 Solidity Ratiod Antennas and open-frame structures • Drag coefficients for lattice tower (Lecture 21) Square cross section with flat-sided members (wind normal to face) 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

22. 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 )

23. 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

24. End of Lecture 23John Holmes225-405-3789 JHolmes@lsu.edu