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Wind tunnel tests on wind loads acting on an angled steel triangular transmission tower
J. Wind Eng. Ind. Aerodyn. 156 (2016) 93–103
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Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Wind tunnel tests on wind loads acting on an angled steel triangular transmission tower Fengli Yang a,n, Huixue Dang b, Huawei Niu c, Hongjie Zhang a, Binrong Zhu a a
China Electric Power Research Institute, Beijing 100192, China School of Civil Engineering, Chang’an University, Xi’an 710061, China c Wind Engineering Research Center, Hunan University, Changsha 410082, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 27 September 2015 Received in revised form 27 June 2016 Accepted 10 July 2016
Wind tunnel tests on scaled models of a triangular transmission tower body made by angled steel members were carried out. The drag coefficients of the total tower body or single frames at nine different test cases were obtained. The experimental results from wind tunnel tests were also mutually validated by computational fluid dynamics (CFD) analysis. The parameters for calculating wind loads on triangular tower bodies determined by wind tunnel tests were compared with the calculated values by some applicable design standards. For the regular triangular tower body with an equivalent solidity ratio for three lateral faces, the experimental curves of the skewed wind load factor Kθ approximately appear like W shape and symmetrical to the axis of θ ¼ 60°. Kθ is decreased to the minimum value when the wind incidence angle is 40° or 80°. When the solidity ratio of face A is different from the other two faces, the symmetry axis of the skewed wind load factor Kθ is shifted to θ ¼ 50°. Kθ is decreased to the minimum value when the wind incidence angle is 30° or 70°. The varying trend of Kθ, especially for the wind incidence angle corresponding to the minimum Kθ value in British standard, are quite different from the experimental results. Based on a combination of the drag coefficient of single frames and the shielding effect factor, a calculation method for the effective projected areas of triangular tower bodies was proposed. Especially for the wind incidence angle θ of 0° or 120°, the calculated values of the effective projected areas agree well with the experimental values obtained from the total tower-body models. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Triangular transmission tower Drag coefficient Skewed wind Shielding effect Wind tunnel test
1. Introduction The traditional transmission towers are usually square or rectangular section structures. With the rapid urbanization in recent years, transmission line corridors have been constrained for more and more limitations. Therefore new types of transmission towers with smaller foundation occupation should be innovated and applied. Triangular section transmission towers can reduce the occupied area significantly. The triangular transmission tower takes the advantages of high structural stability and light weight characteristic. The 60° angled steels or tubular steels are usually used as main members of triangular transmission towers. Transmission tower is one of the most wind-sensitive structures. Wind load is one of the main control load case of transmission towers. In the worldwide, many accidents including structural damage and even collapse of transmission towers have been induced by strong wind (Xie et al., 2006; Holmes, 2008). Wind loads play very important role for the structural design of transmission towers. Thus, the n
Corresponding author.
http://dx.doi.org/10.1016/j.jweia.2016.07.016 0167-6105/& 2016 Elsevier Ltd. All rights reserved.
parameter values and the calculation methods for the wind loads are at the fundamentals of the structural design of transmission towers. In the applicable design standards (ASCE, 1991; ASCE, 2010; AS/ NZS 7000, 2010; BS-8100, 1986; DL/T 5154-2012, 2012; EN 50,34150,341, 2012; IEC 60826, 2003; JEC-127-1979, 1979) for transmission lines, the regulations on the wind loads for square and rectangular section towers are very detailedly presented. Different calculation methods of the drag coefficients and the skewed wind load factors are proposed, and the items are basically consistent in different standards. In order to compare with the regulations in applicable standards conveniently, when the wind direction is normal to a lateral face of the triangular transmission tower, the wind direction is defined as 0° incidence angle. Only ASCE and British design standard specially specify the calculation methods for triangular transmission towers. However, the regulations on skewed wind loads of triangular transmission towers are not proposed in ASCE design standard. The wind incidence angle corresponding to the minimum wind load is 60° as specified in British standard. In Australia/New Zealand structural design
F. Yang et al. / J. Wind Eng. Ind. Aerodyn. 156 (2016) 93–103
2. Wind tunnel test survey and test models 2.1. Test survey The top tower body of a tangent triangular transmission tower of a 220 kV double circuit transmission line was selected for wind tunnel test. The location of the test segment is presented as Fig.1 (a). The wind tunnel tests were completed in the HD-2 wind tunnel of Hunan University (China). The dimension of the HD-2 wind tunnel is 3.0 m in width and 2.5 m in height. The range of the wind speed is from 0 m/s to 58 m/s. All experiments were carried out in smooth flow. The nonuniformity of the wind velocity field in the test region is within 1%. The turbulence intensity of the smooth flow is not higher than 0.2%. The reference height of the mean wind speed is 0.5 m. The force measuring equipment is a shaft type strain-gauge balance with six components developed by China Aerodynamics Research and Development Center (CARDC). The signal collecting and analyzing system can synchronously collect the signals from six force components of the balance realtimely.
Location of the test segment
0.257
2.5
standard (AS/NZS 1170.2, 2011), the drag coefficients of regular triangular towers at 0° wind incidence angle are proposed. In Chinese structural design standard (GB 50,009-52012, 2012), the drag coefficients of regular triangular towers at 0°, 60° and 180° wind incidence angle are specified. However the drag coefficients are identical for three wind incidence angles, which are not well agreed with the actual conditions and may be oversimplified. In order to calculate the wind loads acting on triangular transmission towers more accurately, some research works should be carried on by CFD analysis and wind tunnel tests. Especially for some key design parameters including the drag coefficients, the shielding factors and the skewed wind load factors, which can bring theory reference for the wind resistance design of triangular transmission towers, and great attentions should be paid. Only a few research works have been carried out on the wind loads acting on triangular section tower structures in the worldwide. Some researchers have studied the global drag coefficients of the triangular towers by wind tunnel tests. Mara and Galsworthy (2011) completed a series of wind tunnel tests on a typical 3-dimensional lattice frame at a scale of 1:8, which were compared to those measured for the corresponding prototype under similar flow conditions in a full-scale wind tunnel. The drag coefficients were calculated and used to compare the results from the two experiments for 0°, 30°, 60° and 90° wind incidence angles. The conclusion was reached that model-scale section tests are successful in evaluating the drag coefficient of a triangular-section lattice frame, and are comparable to those of the prototype. Reynolds number mismatches between the two experiments may have had a small influence both on the individual member drag forces and the overall group effect. Akira Hayakawa et al. (2003) proposed a practical method to estimate wind forces acting on a triangular tower with ancillary structures including cables, ladder, etc. This method was verified by comparing with British standard. The drag coefficients of a circular cylinder column in the supercritical region were evaluated by dividing it into two areas, which are the area of the column near a joint does not exhibit the Reynolds number effect and the area of that do exhibit it. C.T. Georgakis et al. (2011) carried out wind-tunnel tests on full-scale sections of four triangular lattice mast configurations. It shows that drag coefficients derived from scaled tests by Whitbread (1977) in the 1970s might need to be re-examined. Drag coefficients for masts subject to smooth flow are generally underestimated, while those same coefficients under turbulent flow are overestimated. The above research results can provide important references for evaluating the wind loads acting on triangular transmission towers. However it is worthy noticing that the shielding effect factors as well as the skewed wind loads acting on triangular towers have not been specially investigated. In particularly, the wind incidence angle corresponding to the minimum wind load proposed by Mara and Galsworthy (2011) is not consistent with the British standard. In this paper, a series of wind tunnel tests on scaled body models and single frame models of a triangular transmission tower made by angled steel members were carried out. Under different wind incidence angles, the drag coefficients of the total tower body or single frames with three solidity ratios for nine test cases were obtained. The experimental results from wind tunnel tests were also mutually validated by CFD analysis. Based on the wind tunnel test results and CFD analysis results, the design parameters including the drag coefficient, the shielding factor as well as the skewed wind load factor were analyzed. The parameters for calculating wind loads on triangular tower bodies determined by wind tunnel tests were compared with the calculated values by some applicable standards. Some suggestions on calculating the wind loads of triangular towers were proposed.
Top compensating segment
0.26 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.26
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Main members The third force-test segment (from top to bottom) Auxiliary members Diagonal members
Bottom compensating segment 0.433
Fig. 1. Dimensions of the test model (Unit: m).
F. Yang et al. / J. Wind Eng. Ind. Aerodyn. 156 (2016) 93–103
The wind tunnel test on the drag coefficients of tower bodies belongs to force measuring tests of rigid models. The reducedscale model should have sufficient stiffness to ensure stability of the measuring forces in the wind tunnel tests. The stainless steel with high elastic modulus of 210 GPa was applied to make the wind tunnel test models. The 60° angle members and 90° angled members were used for making the test models. The main members are connected with both the diagonal members and the auxiliary members by bolts. In the wind tunnel test for every test case, the root mean square (RMS) and the mean value of the measured forces were obtained. The RMS curve appears stable waveform and it has little effect on the mean value of wind forces acting on the tested models. It demonstrates that the tested models have sufficient stiffness to ensure stability of the force measuring in the wind tunnel tests. Therefore the boundary stiffness and constraint conditions have little effect on the test segment. Furthermore, the test segment was constrained at the end of top compensating segment and bottom compensating segment, respectively. The effect of the boundary layer of the wind tunnel can be eliminated by setting these two compensating segments. As shown in Fig.1(b), the scaled ratio of the tower body model is 1:7. The maximum width of the test model at the bottom is 0.433 m. The overall height of the model is 2.5 m. The height of the top and the bottom compensating segments of the test model is 0.26 m. The middle part including nine segments is used for the force test. The height of the force test segment is 1.98 m. 2.2. Test models The test model of the triangular transmission tower consists of three lateral faces, which are named as face A, face B and face C, respectively. The sectional profile of the tower body is shown in Fig.2. The solidity ratios of three lateral faces are ϕA , ϕB and ϕC , respectively. In the process of making test models, the size and geometrical dimensions of three main members were not changed. Variation of the solidity ratio can be adjusted by changing the size of diagonal members or supplying auxiliary members for each segment. Arrangement of the auxiliary members is presented in Fig.1(b). In order to evaluate the effect of solidity ratio on aerodynamic characteristics of the triangular tower body, three frequently used solidity ratios including ϕ1 ¼0.2, ϕ2 ¼0.3 and ϕ3 ¼0.4 were selected. The cases for a tower body with different solidity ratios of face A, face B and face C were also considered. Geometrical dimensions of the main members, the diagonal members and the auxiliary members of the test models are listed in Table 1. When the solidity ratio is 0.2, the auxiliary members are not needed for constructing the test models. The aerodynamic forces of the tower body in Fig. 3(b) can be
95
Table 1 Geometrical dimensions of model members. Solidity ratio ϕ
Main members
Diagonal members
Auxiliary members
0.2 0.3 0.4
∠60° 20 1.5 ∠60° 20 1.5 ∠60° 20 1.5
∟90° 8 1.0 ∟90° 13 1.0 ∟90° 22 1.0
/ ∟90° 13 1.0 ∟90° 13 1.0
obtained by the measured values of the total model in Fig. 1 (b) subtracting the measured values of the top and the bottom compensating segments in Fig. 3(a). In order to investigate the shielding effects on the leeward faces of the triangular tower body, only the windward face A was fixed on the balance and the drag force can be measured. Photos of the single frame model of face A corresponding to three solidity ratios in Table 1 are presented in Fig. 4. 2.3. Test cases The wind incidence angle θ in the wind tunnel test is demonstrated in Fig. 5. It is assumed that when θ ¼0°, the windward face is face A, and the other two faces are named by face B and face C in counter-clockwise direction. For the purpose of investigating the characteristics of the drag coefficient, the shielding effect and the skewed wind loads of triangular transmission towers, nine test cases were designed for this study. Illustration of the test cases is shown in Table 2. It is not realistic to consider fully different solidity ratios for the three tower forces. As shown Table 2, only two types of solidity ratios were considered in this experimental study. One type is that three faces with an equivalent solidity ratio (example for Case 1, Case 2 and Case 3 in Table 2). The other type is that the solidity ratio of face A is different from the other two faces (example for Case 4, Case 5 and Case 6 in Table 2). For practice design of transmission towers, when the cross arms are arranged as Fig. 6, the section of the triangular tower body is usually designed as an isosceles triangle. The solidity ratio of face A is usually different from the other two faces, while the solidity ratio of Face B is equal to Face C. The first six test cases from Case 1 to Case 6 were used to investigate the global drag coefficient of the tower body. Two mean wind speeds of V¼ 20 m/s and V¼30 m/s were considered in Case 2, which was adopted for evaluating the effect of wind velocity on an angled steel tower body. The last three test cases from Case 7 to Case 9 were used to obtain the drag coefficients of single lateral faces, which will be employed in the investigation on shielding effects. The interval of the wind incidence angle θ is 5° for Case 2, while an interval of the wind incidence angle θ is 15° for all the other test cases.
3. Experimental results and discussions 3.1. Experimental data process
Face B Bolt
Face C Diagonal members Main members
Face A Fig. 2. Sectional scheme of the tower body.
In order to apply the experimental results for prototype structures, the measured data are processed and expressed by dimensionless parameters including force coefficients and moment coefficients. Only aerodynamic forces are considered in the wind load calculation of transmission towers. Therefore only the data of mean forces are measured and processed. The definition of the wind incidence angle, the body-fitted coordinate system and the wind directional coordinate system are illustrated in Fig. 5. The symbol D and L represents the drag direction and the lift direction, respectively. The positive direction of X axis is towards the wind direction when the wind incidence angle is 0°. At this time, the
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Top compensating segment
Bottom compensating segment
Fig. 3. Photos of the tower body model.
drag force acting on the tower body is negative. The Z axis is perpendicular to the X-Y plane and in the vertical direction. According to the coordinate system illustrated in Fig. 5, the dimensionless force coefficients in three directions can be calculated by the equation:
Ci = Fi/( 0.5ρV 2S )
(1)
where i¼X, Y, Z, which are the three main directions in body-fitted coordinate system. Fi and Ci are the aerodynamic force and the aerodynamic force coefficient corresponding to the ith direction. V is the mean wind speed used in this experiment, taken as 20 m/s or 30 m/s, respectively. ρ is free stream density, 1.225 kg/m3. S is the reference area, which is defined as the projected area of lateral windward face (face A) of the tower body model when the wind incidence angle is 0°. In Fig. 5, for a wind incidence angle of θ, the global drag coefficient the tower body model in wind directional axis is expressed by CDθ. It can be obtained by combination of the drag force coefficients in body-fitted axis by Eq. (2).
CDθ = ( −CXθ cos θ − CYθ sin θ )
(2)
where CXθ and CYθ are the drag coefficients in X axis and Y axis respectively, which can be calculated by Eq. (1). 3.2. Validation by CFD analysis CFD simulation is one of the most important means to investigate the drag coefficients of lattice steel structures. CFD analysis is a combination technology of modern fluid dynamics, numerical mathematics and computer science. Xie et al. (2010) completed CFD simulations of a rectangular-section angled steel lattice tower under wind loads in different cases based on unstructured meshes. The drag coefficients of the tower bodies with different solidity ratios were obtained. The influences of solidity ratio, wind direction, the ratio of width to height on the wind loads acting on tower bodies were also evaluated. Zhang et al.
(2014) carried out CFD simulations on a square-section angled steel lattice tower under downburst based on structured grids. Global drag coefficients of the angled steel lattice tower segment were obtained. In order to validate the rationality of the wind tunnel test models as well as the experimental drag coefficients, the third force-test segment (from top to bottom) in Fig.1 was selected for CFD simulating analysis. The FLUENT software was used for CFD analysis of the tested segment. The height of the segment is 0.22 m. The top width and the bottom width of the segment are 0.337 m and 0.353 m, respectively. The sizes and dimensions of main members, diagonal members and auxiliary members in CFD model are fully consistent with the test model. The solidity ratios of three lateral faces are equivalent and valued as 0.3. The intersection angle between the main members and the top wall as well as the bottom wall is 86°. Therefore the flow components in the direction of the top wall and the bottom wall can be ignored. According to the geometrical model, fully structured multi-block patched grids consist of 9.49 million hexahedron elements were generated. Rectangular computational region shown in Fig. 7 (a) was employed, with its velocity inlet boundary, pressure outlet boundary and lateral smooth wall boundary placed 1.1 m away from the axisymmetric axis of the tower body, and the geometrical dimensions of the computational region in length, width and height are 2.2 m, 2.2 m and 0.22 m, respectively. The top wall and the bottom wall are flush with the top and the bottom face of the tower body, respectively. The grids on model surfaces and those at three middle height sections are presented in Fig. 7(b) and (c), respectively. The employed boundary conditions illustrated in Fig. 7(a) are velocity inlet (u¼ 30 m/s, v ¼w¼ 0), non-slip adiabatic wall boundary for section model of tower body, free-slip adiabatic wall for bottom wall, ceiling wall, sidewall, respectively, and back pressure is set for outlet boundary. The back pressure at pressure outlet boundary was set to be standard atmosphere pressure (1.01325 105 Pa). In order to well capture the flow characteristics in the near-wall zone, the shear stress transport (SST) k-ω
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97
Fig. 5. Definition of the coordinate system and the wind incidence angle.
Table 2 Illustrations on the wind tunnel test cases. Case number
Face A
Face B
Face C
V(m/s)
θ(°)
1 2 3 4 5 6 7 8 9
ϕ1 ϕ2 ϕ3 ϕ1 ϕ1 ϕ2 ϕ1 ϕ2 ϕ3
ϕ1 ϕ2 ϕ3 ϕ2 ϕ3 ϕ3 / / /
ϕ1 ϕ2 ϕ3 ϕ2 ϕ3 ϕ3 / / /
20 20, 30 20 20 20 20 20 20 20
0 180° 0 180° 0 180° 0 180° 0 180° 0 180° 0 360° 0 360° 0 360°
Face B
Cross arm
Face A
Face C
Cross arm
Fig.6. Illustration of the sectional property of triangular tower body.
Fig. 4. Photos of the single frame model of face A.
turbulence model was employed. Both the inviscid and viscous terms of Navier-Stokes equations were discretized by using the second-order upwind scheme. The Standard scheme and the
SIMPLEC scheme were selected for pressure interpolation and velocity-pressure coupling, respectively. For different wind incidence angles, the surface pressures and the drag force of the tower body can be calculated by using CFD. When the wind incidence angles are θ ¼0° and 30°, the surface pressure contour of the tower body from two view angles is shown in Fig. 8. For wind incidence angle in the range of 0° r θ r60°, the drag coefficients of the triangular tower body calculated by CFD are compared with the experimental values in Table 3 with an angle interval of 10°. It can be seen that the CFD results are basically well agreed with the wind tunnel test values. The maximum relative deviation is not higher than 7%. Especially for the 0° wind incidence angle corresponding to the maximum drag coefficient, the relative variation between the CFD analysis value and the experimental value is only about 0.9%. On this point, a conclusion on the rationality of the wind test model as well as the experimental results can be made. In Table 3, it can also be found that the minimum drag coefficient appears when the wind incidence angle falls in the range from 30° to 40°, resulting in minimum global wind loads acting on the triangular tower segment.
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Velocity inlet
Pressure outlet
2.2m
0.22m 0.11m
Middle height section
2.2m
0.22m Bottom wall Side wall
Section model of tower body
Fig. 7. Grids of the segment model.
3.3. Experimental results and discussion 3.3.1. Global drag coefficients As discussed in Section 3.1, the global drag coefficients of the triangular tower body in wind directional axis can be calculated according to Eq. (2). The global drag coefficient curves for Case 2 under the mean wind speed of V¼20 m/s and V ¼30 m/s are plotted in Fig. 9(a). By considering that the separation points of the air flow passing through angle section members are fixed, the Reynolds number effects on the aerodynamic characteristics of angle section members can be ignored. Therefore the global drag coefficients of the angled steel triangular tower body do not differ significantly at two different mean wind speeds. At the case of the wind incidence angle θ ¼ 120°, the maximum difference between the global drag coefficients under V ¼20 m/s and V ¼30 m/s is only about 4.4%. When the mean wind speed is 20 m/s, the radar graph of the drag coefficients in wind directional axis is plotted as shown in Fig. 9(b). For the equilateral triangular tower body with an
Fig. 8. Pressure contour of the tower body (Unit: Pa). Table 3 Comparison on the drag coefficients by CFD analysis and wind tunnel test. θ(°)
0
10
20
30
40
50
60
Experimental values CFD analysis values
2.15 2.13
2.08 2.05
1.91 1.87
1.72 1.69
1.67 1.70
1.72 1.83
1.74 1.86
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identical solidity ratio of three lateral faces, Fig. 9(b) shows that the global drag coefficient curve is approximately symmetrical to the axis of θ ¼60°. It can be observed that the drag coefficients at the symmetrical wind incidence angles are slightly different. Example for a symmetrical pair of θ ¼30° and θ ¼90°, the corresponding drag coefficient in wind directional axis is 1.71 and 1.68 respectively. The slight differences between the drag coefficient at angles of attack 30° and 90° are attributed to differences in the orientation of the 60° angled steel main members, 90° angled steel diagonal members and auxiliary members (Simon Prud’homme et al., 2014). This similar conclusion can also be verified by the research of Mara and Galsworthy (2011). When the solidity ratios are 0.2 and 0.3, the drag coefficient curves of the triangular tower bodies are presented in Fig. 9(c). It can be seen that the drag coefficient in wind directional axis decrease with the increasing of the solidity ratio, while the varying trends depending on the wind incidence angle are generally consistent. The calculation methods of the drag coefficients of triangular lattice towers are regulated in some standards including ASCE standard (1991, 2010), British standard, Australia/New Zealand structural design standard and Chinese structural design standard. The proposed drag coefficients are generally corresponding to the 0° wind incidence angle. For Case 1, Case 2 and Case 3 of the wind tunnel tests listed in Table 2, the experimental values of the global drag coefficient in wind directional axis are compared with the calculated values by some design standards in Fig. 10. It can be seen that the experimental values are more close to the values calculated by British standard. When the solidity ratios of the lateral faces are 0.2, 0.3 and 0.4, the calculated drag coefficients are higher than the experimental values by 2.0%, 6.9% and 4.7% respectively. The drag coefficients calculated by Chinese structural design standard are all lower than the experimental values. It indicates that the wind loads acting on triangular towers will be underestimated by employing Chinese structural design standard. 3.3.2. Skewed wind load factors By considering the relative intersection angle between the electrical lines and the transmission tower structures, the 0°, 30°, 45° and 90° wind load case usually should be considered in the structural design of transmission towers. The skewed wind load factor Kθ is an important parameter for calculating the skewed wind loads on transmission towers (Mara and Ho, 2011; Yang et al., 2015). All the wind tunnel tests in this study were completed under steady-state flow conditions. The test models are rigid enough to ensure that a slight turbulence effect (the turbulence
Fig. 9. Drag coefficients in wind directional axis.
Fig. 10. Comparison on the drag coefficients.
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F. Yang et al. / J. Wind Eng. Ind. Aerodyn. 156 (2016) 93–103
intensity is within 0.2%) of the wind flow on the drag force can be neglected. The wind loads of transmission tower bodies under skewed wind in ASCE standard, IEC standard and European standard etc. are calculated by:
FDθ =
1 2 ρV CD Ab Kθ 2
(3)
where FDθ is the measured drag force when the wind incidence angle is θ, CD is the drag coefficient when the wind incidence angle is 0°, Ab is the total projected area of the members belong to Face A in Fig. 5. The skewed wind load factor can be calculated by Kθ = CDθ /CD . Only the British standard proposes specific method for calculating the skewed wind load factor of triangular tower bodies. In particularly, the calculation formula of Kθ for the equilateral triangular section tower body with three equivalent lateral faces is as follows:
Kθ =
Abf ⎡ Abc + ⎣ 1 − 0.1 sin2 ( 1.5θ ) ⎤⎦ Ab Ab
(4)
where Abc is the total projected area of the tubular section members, Abf is the total projected area of the angle section members. Especially for the triangular tower bodies fully made of angle section members, Eq. (4) can be simplified as Kθ = ⎡⎣ 1 − 0.1 sin2 ( 1.5θ ) ⎤⎦. For an equilateral triangular section tower body, in a symmetrical period of the wind incidence angle θ from 0° to 120°, the experimental curves of skewed wind load factor Kθ for Case 1 and Case 2 are presented in Fig. 11. It can be seen that the skewed wind load factor calculated by British standard is generally higher than the experimental values. The Kθ curve in British standard is symmetrical to the axis of θ ¼60° and Kθ is decreased to its minimum value when the wind incidence angle is 60°. The experimental curves of the skewed wind load factor Kθ approximately appear like W shape and symmetrical to the axis of θ ¼60°. However Kθ is decreased to its local minimum value when the wind incidence angle is 40° or 80°. In other words, the wind loads acting on the triangular tower body is decreased to the minimum value for these incidence angles. This conclusion can also be validated by the CFD analysis results in Table 3 in Section 3.2. For the convenience of comparing with experimental results and calculated values by British standard, the wind incidence angle of 0°, 30° and 60° in the study by Mara and Galsworthy (2011) can be equivalently transformed to 60°, 30° and 0° as defined in Fig. 5. The wind tunnel test results presented in this study also indicate that the wind
Fig. 11. Comparison of the skewed wind load factors (Face A is equivalent to face B and face C).
incidence angle corresponding to the minimum wind loads acting on a triangular tower body is 30°. Besides the Kθ values calculated by British standard are higher than the experimental values, the shape and the lowest position of the Kθ curve in British standard are different from the experimental curves. It demonstrates that the skewed wind load factor calculated by British standard for some wind incidence angles may be oversimplified and inaccurate. The calculation formula such as Eq. (4) given by British standard should be improved. When the solidity ratio of face A is different from the other two faces (example for Case 4, Case 5 and Case 6), the skewed wind load factor Kθ for θ in the range from 0° to 120° is defined as:
⎧ CDθ (0o ≤ θ < 60o) ⎪ ⎪ CDA ⎪ 2CDθ (θ = 60o) Kθ = ⎨ C ( ⎪ DA + CDB ) ⎪ CDθ ⎪ (60o < θ ≤ 120o) ⎪ ⎩ CDB
(5)
where CDA, CDB are the global drag coefficients of triangular tower bodies when θ ¼0° and θ ¼120°, respectively. According to Eq. (5), the skewed wind load factor Kθ for Case 4, Case 5 and Case 6 can be calculated and compared with British standard in Fig. 12. Fig. 12 shows that the experimental curves of the skewed wind load factor Kθ still approximately appear like W shape. The symmetry axis of the skewed wind load factor Kθ is shifted near to θ ¼50°. Kθ is decreased to its local minimum value when the wind incidence angle θ is 30° or 70°. The varying trend of Kθ , especially for the wind incidence angle corresponding to the minimum value in British standard, are significantly different from experimental results. The skewed wind load factors calculated by British standard are generally higher than the experimental values. Only when the wind incidence angle is in the range of 50° to 60° for Case 4 and Case 5, the experimental values are higher than the calculated values according to British standard. In these cases, the wind loads acting on triangular tower bodies would be underestimated by employing British standard. 3.3.3. Shielding factors In British standard and Chinese standard, the global drag coefficients of lattice tower bodies can be derived from the drag coefficient of the windward face by considering the effective shielding effect on leeward faces. Comparing to square and
Fig. 12. Comparison of the skewed wind load factors (Face A is different from face B and face C).
F. Yang et al. / J. Wind Eng. Ind. Aerodyn. 156 (2016) 93–103
rectangular-section tower structures, the shielding effect of triangular section tower structures has special characteristics. If face A in Fig. 5 is assumed as the windward face, face B and face C are both leeward faces. The shielding factor of triangular tower should be specially studied. The drag coefficient of face A can be measured by the test model shown in Fig. 4. And based on the global drag coefficient of triangular tower bodies for Case 1, Case 2 and Case 3, the shielding effect of face A on face B and face C were analyzed. The global wind load of a triangular tower body consists of three wind load components acting on three lateral faces. The global wind load on a triangular tower body can be written as:
FWT = FSA + FSB + FSC
(6)
where FWT is the global wind load of a triangular tower body, FSA, FSB and FSC are the wind load acting on the lateral face A, face B and face C respectively. When the wind direction is normal to a lateral face and the wind load acting on this face is FS. For the ith acute angle θi between the wind direction and the lateral face, the wind load acting on this lateral face can be calculated by:
(7)
Fi = FS sin θi
As discussed on triangular tower structures above, the wind loads acting on two leeward faces will be reduced for the shielding effect induced by the windward face. If the wind load acting on face A in Fig. 5 is selected as a reference parameter, Eq. (6) can be written as:
FWT = FSA (sin θiA + ηB sin θiB + ηC sin θiC )
(8)
where ηB and ηC are the shielding factor of face B and face C, respectively. According to Eq. (1), Eq. (8) can be converted to a dimensionless form by employing the item of drag coefficients, and the new expression is given as:
CD = CDA (sin θiA + ηB sin θiB + ηC sin θiC )
(9)
The global drag coefficient of the triangular tower body equals to the maximum value when the wind incidence angle is 0° or 120°. For the convenient use in design process, the drag coefficient under the wind incidence angle θ ¼0° is employed to calculate the shielding factor. Then the global drag coefficient of the triangular tower body can be calculated by:
CD = CDA ( 1 + ηB sin 30o + ηC sin 30o)
(10)
In particularly, for an equilateral triangular section tower body, it can be defined as ηB ¼ ηC ¼ η. The calculation formula of the shielding factor can be written as:
η=
CD −1 CDA
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Table 5 Comparison of the shielding factor η.
ϕ
C¯D
C¯DA
η
0.2 0.3 0.4
2.449 2.080 1.878
1.602 1.384 1.355
0.53 0.50 0.39
θ ¼ 120° and the drag coefficient CDA for θ ¼360° should be fully agreed with the corresponding values for θ ¼ 0°. However, the experimental errors induced by measuring apparatus and model making, can not be fully avoided. Therefore the drag coefficients at corresponding wind incidence angles exhibit slight differences. In order to improve the accuracy of experimental data, the drag coefficients at two corresponding wind incidence angles were averaged. The average value of the global drag coefficient and the drag coefficient of single lateral faces are expressed by C¯D and C¯DA . According to Eq. (11), the shielding factor η can be calculated and listed in Table 5. In British standard, the drag coefficients for single lattice frames made by angle section members, Cnf , is given by:
⎧ 1.8 ϕ ≤ 0.6 ⎪ 1.58 + 1.05 ( 0.6 − ϕ) Cnf = ⎨ 2 ⎪ ⎩ 1.58 + 2.625 ( ϕ − 0.6) ϕ > 0.6
When the solidity ratio ϕ are 0.2, 0.3 and 0.4, the drag coefficient of face A calculated by Eq. (12) are 1.78, 1.70 and 1.64 respectively. The calculated drag coefficients by British standard are higher than the experimental values in Table 5 by 11.1%, 22.8% and 21.0%. In the applicable standards, only the British standard proposes the calculation method of the shielding factors for triangular towers. For the triangular towers fully making by angle section members, the calculation formula of the shielding factor is given by:
η=
2 ( 1 − ϕ)1.89 3
When the wind incidence angle θ ¼ 0°, 120° or 360°, the global drag coefficient CD and the drag coefficient CDA are listed in Table 4. In purely theoretical point, the global drag coefficient CD for Table 4 Drag coefficients of the tower body and the single frame for θ ¼0°. θ(°)
CD
θ(°)
CDA
0.2
0 120
2.409 2.488
0 360
1.669 1.534
0.3
0 120
2.096 2.063
0 360
1.431 1.338
0.4
0 120
1.839 1.917
0 360
1.379 1.331
(13)
In Fig. 13, the experimental shielding factors of triangular tower bodies are compared with the calculated values by Eq. (13) regulated in British standard. When the solidity ratio ϕ are 0.2, 0.3 and 0.4 respectively, the calculated shielding factors by British standard are lower than the experimental values by 17.5%, 32.1% and 34.9%. If it was assumed that the drag coefficients for single lattice frames calculated by Eq. (12) are equivalent to the experimental
(11)
ϕ
(12)
Fig. 13. Comparison on the shielding factors η.
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5. Conclusions and recommendations
Table 6 Comparison on the effective projected areas. Experimental values(m2) Calculated values(m2) Relative variations (%)
Case number
θ(°)
4
0 0.371 120 0.408
0.383 0.444
3.2 8.9
5
0 0.416 120 0.480
0.427 0.495
2.7 3.2
6
0 0.453 120 0.560
0.482 0.508
6.3 9.2
A series of wind tunnel tests on 1:7 scaled body models and single frame models of a triangular transmission tower made by angled steel members were carried out. Under different wind incidence angles, the drag coefficients of the total tower body or single frames with three solidity ratios for nine test cases were obtained. The experimental results from wind tunnel tests were also mutually validated by CFD analysis. The design parameters including the drag coefficient, the shielding factor as well as the skewed wind load factor were analyzed. The main findings are summarized as follows:
For the equilateral triangular tower body with an identical so-
values, the global wind loads acting on triangular tower bodies would be underestimated by British standard. Based on the above analysis, the drag coefficients of single lattice frames calculated by British standard are lower than the experimental values, and the shielding factors are in a reverse turn. While the increasing extents of the shielding factors are higher than the decreasing extents of the drag coefficients of single lattice frames, it can be concluded that the global drag coefficients calculated by British standard are higher than the experimental values according to Eq. (9). This conclusion can also be verified by the comparison analysis in Fig.10.
4. Additional results-application on effective projected areas When the solidity ratio of face A is different from the other two faces, the projected areas of the members of windward faces are not identical for calculating the global drag coefficients under different wind directions. Therefore it is difficult to calculate the global drag coefficients by the drag coefficients of single lateral faces. The parameter CD Ap which usually called effective projected area (EPA) was proposed and employed to evaluate the wind loads acting on triangular towers with three different lateral faces. According to the Eq. (4), (Eq. (6) and 7), when the wind incidence angle θ ¼0° and θ ¼120°, the effective projected areas of the triangular tower bodies can be given as:
( CD Ap )θ= 0o = CDA ApA + ( CD Ap )θ= 120o = CDB ApB
ηA ( CDB ApB + CDC ApC ) 2 ηB + ( CDC ApC + CDA ApA ) 2
lidity ratio for three lateral faces, the global drag coefficient curve is approximately symmetrical to the axis of θ ¼60°. When the wind incidence angle is 0°, the experimental drag coefficients are more close to the calculated values by British standard. When the solidity ratios of the lateral faces are 0.2, 0.3 and 0.4, the calculated drag coefficient are higher than the experimental values by 2.0%, 6.9% and 4.7% respectively. The wind loads acting on triangular towers will be underestimated by Chinese structural design standard. For the equilateral triangular tower body with an identical solidity ratio for three lateral faces, the experimental curves of the skewed wind load factor Kθ approximately appear like W shape and symmetrical to the axis of θ ¼ 60°. Kθ is decreased to its local minimum value when the wind incidence angle is 40° or 80°. When the solidity ratio of face A is different from the other two faces, the symmetry axis of Kθ is shifted to θ ¼50°. Kθ is decreased to its minimum value when the wind incidence angle is 30° or 70°. The varying trend of Kθ , especially for the wind incidence angle corresponding to the minimum value in British standard, are quite different from experimental results. When the wind incidence angle is in the range of 50° to 60° for some test cases, the wind loads acting on triangular tower bodies would be underestimated by employing British standard. Based on a combination of the drag coefficient of single frames and the shielding effect factor, a calculation method of the effective projected areas for triangular tower bodies was proposed. When the wind incidence angle θ is 0° or 120°, the calculated values of the effective projected areas agree well with the experimental values by the total tower-body models.
(14)
where CDA, CDB and CDC are the drag coefficients of the single lateral face A, face B and face C, ηB and ηC are the shielding factor of face B and face C respectively, and these five parameters can be valued according to Table 5. ApA, ApB and ApC are the projected areas of the single lateral face A, face B and face C respectively. When the solidity ratios are 0.2, 0.3 and 0.4, the corresponding projected areas are 0.137 m2, 0.205 m2 and 0.372 m2 respectively. At the case of the wind incidence angle is θ ¼0° or θ ¼120°, the effective projected areas determined by the wind tunnel tests on global models as well as the calculated values by Eq. (14) are listed in Table 6. By employing the drag coefficients of single lateral faces and the shielding factors η, the effective projected areas calculated by Eq. (14) are generally agreed well with the experimental values by global test models. The relative variations are in a range from 9.2% to 2.7%. It indicates that Eq. (14) is suitable for calculating the global wind loads on triangular tower bodies. Except for θ ¼120° under Case 6, the calculated effective projected areas are higher than the experimental values. The global wind loads acting on triangular tower bodies calculated by Eq. (14) are generally conservative and may induce more safe design.
Acknowledgements This work has been funded by the financial support from National Natural Science Foundation of China (51408568, 51308519) and State Grid Corporation of China. The authors would like to thank the sponsors.
References Akira Hayakawa, Takeshi Ohkuma, Kazutsugu Hiramatsu, et al., 2003. Characteristics of wind forces on a triangular telecommunications steel tower. 11th International Conference on Wind Engineering, IAWE, Texas, USA. American Society of Civil Engineers (ASCE), 1991. ASCE manuals and reports on engineering practice No.74. Reston, American. American Society of Civil Engineers (ASCE), 2010. ASCE manuals and reports on engineering practice No.74. Reston, American. AS/NZS 1170.2, 2011. Structural Design Actions: Part 2-Wind actions. Standards Australia Limited/Standards New Zealand, Sydney, Australian. AS/NZS 7000, 2010. Overhead line design-Detailed procedures. Standards Australia Limited/Standards New Zealand, Sydney, Australian. BS-8100, 1986. Lattice tower and masts-Part1: Code of practice for loading. British Standards Institution, London, Britain.
F. Yang et al. / J. Wind Eng. Ind. Aerodyn. 156 (2016) 93–103
DL/T 5154-2012, 2012. Technical code for the design of tower and pole structures of overhead transmission lines. China Planning Press, Beijing, China, in Chinese. EN 50341-50341, 2012. Overhead electrical lines exceeding AC 1kV-Part 1: General requirement—common specifications. European Committee for Electrotechnical Standardization, Brussels, Belgium. GB 50009-52012, 2012. Load code for the design of building structures. China Architecture and Building Press, Beijing, China, in Chinese. Georgakis, C.T., Støttrup-Andersen, U., Johnsen, M., et al., 2011. Drag coefficients of lattice masts from full-scale wind-tunnel tests. 5th European and African Conference on Wind Engineering, Florence, Italy. Holmes, J.D., 2008. Recent developments in the specification of wind loads on transmission lines. J. Wind Eng. 5 (1), 8–18. IEC 60826, 2003. Design criteria of overhead transmission lines. International Electrotechnical Commission, Geneva, Switzerland. JEC-127-1979, 1979. Design Standards on Structures for Transmissions. Japanese Electrotechnical Committee, Tokyo, Japan, in Japanese. Mara, T.G., Ho, T.C.E., 2011. Design loads for transmission towers under skewed wind loading. Struct. Congr. 2011 © ASCE 2011, 1246–1257. Mara, T.G., Galsworthy, J.K., 2011. Comparison of model-scale and full-scale wind
103
tunnel test results for a typical 3-dimensional lattice frame. 13th International Conference on Wind Engineering, Amsterdam, NL. Prud’homme, Simon, Legeron, Frederic, Laneville, Andre, et al., 2014. Wind forces on single and shielded angle members in lattice structures. J. Wind Eng. Ind. Aerodyn. 124, 20–28. Whitbread, R.E., 1977. Wind Loading on Lattice Towers, Report on Project Number P352003, National Maritime Institute, UK. Xie, H.P., He, M.J., Ma, R.L., 2010. Analysis of mean wind load of lattice tower based on CFD simulation. J. Cent. South Univ. (Sci. Technol.) 41 (5), 1980–1986, in Chinese. Xie, Q., Zhang, Y., Li, J., 2006. Investigation on tower collapses of 500kV RenShang 5237 transmission line caused by downburst. Power Syst. Technol. 30 (10), 59–63, in Chinese. Yang, Fengli, Yang, Jingbo, Niu, Huawei, et al., 2015. Design wind loads for tubularangle steel cross-arms of transmission towers under skewed wind loading. J. Wind Eng. Ind. Aerodyn. 140, 10–18. Zhang, L., Li, J., Dang, H.X., 2014. Investigation of wind loads of lattice tower in downburst. Chinese. J. Appl. Mech. 31 (3), 343–347, in Chinese.
Contents lists available at ScienceDirect
Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Wind tunnel tests on wind loads acting on an angled steel triangular transmission tower Fengli Yang a,n, Huixue Dang b, Huawei Niu c, Hongjie Zhang a, Binrong Zhu a a
China Electric Power Research Institute, Beijing 100192, China School of Civil Engineering, Chang’an University, Xi’an 710061, China c Wind Engineering Research Center, Hunan University, Changsha 410082, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 27 September 2015 Received in revised form 27 June 2016 Accepted 10 July 2016
Wind tunnel tests on scaled models of a triangular transmission tower body made by angled steel members were carried out. The drag coefficients of the total tower body or single frames at nine different test cases were obtained. The experimental results from wind tunnel tests were also mutually validated by computational fluid dynamics (CFD) analysis. The parameters for calculating wind loads on triangular tower bodies determined by wind tunnel tests were compared with the calculated values by some applicable design standards. For the regular triangular tower body with an equivalent solidity ratio for three lateral faces, the experimental curves of the skewed wind load factor Kθ approximately appear like W shape and symmetrical to the axis of θ ¼ 60°. Kθ is decreased to the minimum value when the wind incidence angle is 40° or 80°. When the solidity ratio of face A is different from the other two faces, the symmetry axis of the skewed wind load factor Kθ is shifted to θ ¼ 50°. Kθ is decreased to the minimum value when the wind incidence angle is 30° or 70°. The varying trend of Kθ, especially for the wind incidence angle corresponding to the minimum Kθ value in British standard, are quite different from the experimental results. Based on a combination of the drag coefficient of single frames and the shielding effect factor, a calculation method for the effective projected areas of triangular tower bodies was proposed. Especially for the wind incidence angle θ of 0° or 120°, the calculated values of the effective projected areas agree well with the experimental values obtained from the total tower-body models. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Triangular transmission tower Drag coefficient Skewed wind Shielding effect Wind tunnel test
1. Introduction The traditional transmission towers are usually square or rectangular section structures. With the rapid urbanization in recent years, transmission line corridors have been constrained for more and more limitations. Therefore new types of transmission towers with smaller foundation occupation should be innovated and applied. Triangular section transmission towers can reduce the occupied area significantly. The triangular transmission tower takes the advantages of high structural stability and light weight characteristic. The 60° angled steels or tubular steels are usually used as main members of triangular transmission towers. Transmission tower is one of the most wind-sensitive structures. Wind load is one of the main control load case of transmission towers. In the worldwide, many accidents including structural damage and even collapse of transmission towers have been induced by strong wind (Xie et al., 2006; Holmes, 2008). Wind loads play very important role for the structural design of transmission towers. Thus, the n
Corresponding author.
http://dx.doi.org/10.1016/j.jweia.2016.07.016 0167-6105/& 2016 Elsevier Ltd. All rights reserved.
parameter values and the calculation methods for the wind loads are at the fundamentals of the structural design of transmission towers. In the applicable design standards (ASCE, 1991; ASCE, 2010; AS/ NZS 7000, 2010; BS-8100, 1986; DL/T 5154-2012, 2012; EN 50,34150,341, 2012; IEC 60826, 2003; JEC-127-1979, 1979) for transmission lines, the regulations on the wind loads for square and rectangular section towers are very detailedly presented. Different calculation methods of the drag coefficients and the skewed wind load factors are proposed, and the items are basically consistent in different standards. In order to compare with the regulations in applicable standards conveniently, when the wind direction is normal to a lateral face of the triangular transmission tower, the wind direction is defined as 0° incidence angle. Only ASCE and British design standard specially specify the calculation methods for triangular transmission towers. However, the regulations on skewed wind loads of triangular transmission towers are not proposed in ASCE design standard. The wind incidence angle corresponding to the minimum wind load is 60° as specified in British standard. In Australia/New Zealand structural design
F. Yang et al. / J. Wind Eng. Ind. Aerodyn. 156 (2016) 93–103
2. Wind tunnel test survey and test models 2.1. Test survey The top tower body of a tangent triangular transmission tower of a 220 kV double circuit transmission line was selected for wind tunnel test. The location of the test segment is presented as Fig.1 (a). The wind tunnel tests were completed in the HD-2 wind tunnel of Hunan University (China). The dimension of the HD-2 wind tunnel is 3.0 m in width and 2.5 m in height. The range of the wind speed is from 0 m/s to 58 m/s. All experiments were carried out in smooth flow. The nonuniformity of the wind velocity field in the test region is within 1%. The turbulence intensity of the smooth flow is not higher than 0.2%. The reference height of the mean wind speed is 0.5 m. The force measuring equipment is a shaft type strain-gauge balance with six components developed by China Aerodynamics Research and Development Center (CARDC). The signal collecting and analyzing system can synchronously collect the signals from six force components of the balance realtimely.
Location of the test segment
0.257
2.5
standard (AS/NZS 1170.2, 2011), the drag coefficients of regular triangular towers at 0° wind incidence angle are proposed. In Chinese structural design standard (GB 50,009-52012, 2012), the drag coefficients of regular triangular towers at 0°, 60° and 180° wind incidence angle are specified. However the drag coefficients are identical for three wind incidence angles, which are not well agreed with the actual conditions and may be oversimplified. In order to calculate the wind loads acting on triangular transmission towers more accurately, some research works should be carried on by CFD analysis and wind tunnel tests. Especially for some key design parameters including the drag coefficients, the shielding factors and the skewed wind load factors, which can bring theory reference for the wind resistance design of triangular transmission towers, and great attentions should be paid. Only a few research works have been carried out on the wind loads acting on triangular section tower structures in the worldwide. Some researchers have studied the global drag coefficients of the triangular towers by wind tunnel tests. Mara and Galsworthy (2011) completed a series of wind tunnel tests on a typical 3-dimensional lattice frame at a scale of 1:8, which were compared to those measured for the corresponding prototype under similar flow conditions in a full-scale wind tunnel. The drag coefficients were calculated and used to compare the results from the two experiments for 0°, 30°, 60° and 90° wind incidence angles. The conclusion was reached that model-scale section tests are successful in evaluating the drag coefficient of a triangular-section lattice frame, and are comparable to those of the prototype. Reynolds number mismatches between the two experiments may have had a small influence both on the individual member drag forces and the overall group effect. Akira Hayakawa et al. (2003) proposed a practical method to estimate wind forces acting on a triangular tower with ancillary structures including cables, ladder, etc. This method was verified by comparing with British standard. The drag coefficients of a circular cylinder column in the supercritical region were evaluated by dividing it into two areas, which are the area of the column near a joint does not exhibit the Reynolds number effect and the area of that do exhibit it. C.T. Georgakis et al. (2011) carried out wind-tunnel tests on full-scale sections of four triangular lattice mast configurations. It shows that drag coefficients derived from scaled tests by Whitbread (1977) in the 1970s might need to be re-examined. Drag coefficients for masts subject to smooth flow are generally underestimated, while those same coefficients under turbulent flow are overestimated. The above research results can provide important references for evaluating the wind loads acting on triangular transmission towers. However it is worthy noticing that the shielding effect factors as well as the skewed wind loads acting on triangular towers have not been specially investigated. In particularly, the wind incidence angle corresponding to the minimum wind load proposed by Mara and Galsworthy (2011) is not consistent with the British standard. In this paper, a series of wind tunnel tests on scaled body models and single frame models of a triangular transmission tower made by angled steel members were carried out. Under different wind incidence angles, the drag coefficients of the total tower body or single frames with three solidity ratios for nine test cases were obtained. The experimental results from wind tunnel tests were also mutually validated by CFD analysis. Based on the wind tunnel test results and CFD analysis results, the design parameters including the drag coefficient, the shielding factor as well as the skewed wind load factor were analyzed. The parameters for calculating wind loads on triangular tower bodies determined by wind tunnel tests were compared with the calculated values by some applicable standards. Some suggestions on calculating the wind loads of triangular towers were proposed.
Top compensating segment
0.26 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.22 0.26
94
Main members The third force-test segment (from top to bottom) Auxiliary members Diagonal members
Bottom compensating segment 0.433
Fig. 1. Dimensions of the test model (Unit: m).
F. Yang et al. / J. Wind Eng. Ind. Aerodyn. 156 (2016) 93–103
The wind tunnel test on the drag coefficients of tower bodies belongs to force measuring tests of rigid models. The reducedscale model should have sufficient stiffness to ensure stability of the measuring forces in the wind tunnel tests. The stainless steel with high elastic modulus of 210 GPa was applied to make the wind tunnel test models. The 60° angle members and 90° angled members were used for making the test models. The main members are connected with both the diagonal members and the auxiliary members by bolts. In the wind tunnel test for every test case, the root mean square (RMS) and the mean value of the measured forces were obtained. The RMS curve appears stable waveform and it has little effect on the mean value of wind forces acting on the tested models. It demonstrates that the tested models have sufficient stiffness to ensure stability of the force measuring in the wind tunnel tests. Therefore the boundary stiffness and constraint conditions have little effect on the test segment. Furthermore, the test segment was constrained at the end of top compensating segment and bottom compensating segment, respectively. The effect of the boundary layer of the wind tunnel can be eliminated by setting these two compensating segments. As shown in Fig.1(b), the scaled ratio of the tower body model is 1:7. The maximum width of the test model at the bottom is 0.433 m. The overall height of the model is 2.5 m. The height of the top and the bottom compensating segments of the test model is 0.26 m. The middle part including nine segments is used for the force test. The height of the force test segment is 1.98 m. 2.2. Test models The test model of the triangular transmission tower consists of three lateral faces, which are named as face A, face B and face C, respectively. The sectional profile of the tower body is shown in Fig.2. The solidity ratios of three lateral faces are ϕA , ϕB and ϕC , respectively. In the process of making test models, the size and geometrical dimensions of three main members were not changed. Variation of the solidity ratio can be adjusted by changing the size of diagonal members or supplying auxiliary members for each segment. Arrangement of the auxiliary members is presented in Fig.1(b). In order to evaluate the effect of solidity ratio on aerodynamic characteristics of the triangular tower body, three frequently used solidity ratios including ϕ1 ¼0.2, ϕ2 ¼0.3 and ϕ3 ¼0.4 were selected. The cases for a tower body with different solidity ratios of face A, face B and face C were also considered. Geometrical dimensions of the main members, the diagonal members and the auxiliary members of the test models are listed in Table 1. When the solidity ratio is 0.2, the auxiliary members are not needed for constructing the test models. The aerodynamic forces of the tower body in Fig. 3(b) can be
95
Table 1 Geometrical dimensions of model members. Solidity ratio ϕ
Main members
Diagonal members
Auxiliary members
0.2 0.3 0.4
∠60° 20 1.5 ∠60° 20 1.5 ∠60° 20 1.5
∟90° 8 1.0 ∟90° 13 1.0 ∟90° 22 1.0
/ ∟90° 13 1.0 ∟90° 13 1.0
obtained by the measured values of the total model in Fig. 1 (b) subtracting the measured values of the top and the bottom compensating segments in Fig. 3(a). In order to investigate the shielding effects on the leeward faces of the triangular tower body, only the windward face A was fixed on the balance and the drag force can be measured. Photos of the single frame model of face A corresponding to three solidity ratios in Table 1 are presented in Fig. 4. 2.3. Test cases The wind incidence angle θ in the wind tunnel test is demonstrated in Fig. 5. It is assumed that when θ ¼0°, the windward face is face A, and the other two faces are named by face B and face C in counter-clockwise direction. For the purpose of investigating the characteristics of the drag coefficient, the shielding effect and the skewed wind loads of triangular transmission towers, nine test cases were designed for this study. Illustration of the test cases is shown in Table 2. It is not realistic to consider fully different solidity ratios for the three tower forces. As shown Table 2, only two types of solidity ratios were considered in this experimental study. One type is that three faces with an equivalent solidity ratio (example for Case 1, Case 2 and Case 3 in Table 2). The other type is that the solidity ratio of face A is different from the other two faces (example for Case 4, Case 5 and Case 6 in Table 2). For practice design of transmission towers, when the cross arms are arranged as Fig. 6, the section of the triangular tower body is usually designed as an isosceles triangle. The solidity ratio of face A is usually different from the other two faces, while the solidity ratio of Face B is equal to Face C. The first six test cases from Case 1 to Case 6 were used to investigate the global drag coefficient of the tower body. Two mean wind speeds of V¼ 20 m/s and V¼30 m/s were considered in Case 2, which was adopted for evaluating the effect of wind velocity on an angled steel tower body. The last three test cases from Case 7 to Case 9 were used to obtain the drag coefficients of single lateral faces, which will be employed in the investigation on shielding effects. The interval of the wind incidence angle θ is 5° for Case 2, while an interval of the wind incidence angle θ is 15° for all the other test cases.
3. Experimental results and discussions 3.1. Experimental data process
Face B Bolt
Face C Diagonal members Main members
Face A Fig. 2. Sectional scheme of the tower body.
In order to apply the experimental results for prototype structures, the measured data are processed and expressed by dimensionless parameters including force coefficients and moment coefficients. Only aerodynamic forces are considered in the wind load calculation of transmission towers. Therefore only the data of mean forces are measured and processed. The definition of the wind incidence angle, the body-fitted coordinate system and the wind directional coordinate system are illustrated in Fig. 5. The symbol D and L represents the drag direction and the lift direction, respectively. The positive direction of X axis is towards the wind direction when the wind incidence angle is 0°. At this time, the
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Top compensating segment
Bottom compensating segment
Fig. 3. Photos of the tower body model.
drag force acting on the tower body is negative. The Z axis is perpendicular to the X-Y plane and in the vertical direction. According to the coordinate system illustrated in Fig. 5, the dimensionless force coefficients in three directions can be calculated by the equation:
Ci = Fi/( 0.5ρV 2S )
(1)
where i¼X, Y, Z, which are the three main directions in body-fitted coordinate system. Fi and Ci are the aerodynamic force and the aerodynamic force coefficient corresponding to the ith direction. V is the mean wind speed used in this experiment, taken as 20 m/s or 30 m/s, respectively. ρ is free stream density, 1.225 kg/m3. S is the reference area, which is defined as the projected area of lateral windward face (face A) of the tower body model when the wind incidence angle is 0°. In Fig. 5, for a wind incidence angle of θ, the global drag coefficient the tower body model in wind directional axis is expressed by CDθ. It can be obtained by combination of the drag force coefficients in body-fitted axis by Eq. (2).
CDθ = ( −CXθ cos θ − CYθ sin θ )
(2)
where CXθ and CYθ are the drag coefficients in X axis and Y axis respectively, which can be calculated by Eq. (1). 3.2. Validation by CFD analysis CFD simulation is one of the most important means to investigate the drag coefficients of lattice steel structures. CFD analysis is a combination technology of modern fluid dynamics, numerical mathematics and computer science. Xie et al. (2010) completed CFD simulations of a rectangular-section angled steel lattice tower under wind loads in different cases based on unstructured meshes. The drag coefficients of the tower bodies with different solidity ratios were obtained. The influences of solidity ratio, wind direction, the ratio of width to height on the wind loads acting on tower bodies were also evaluated. Zhang et al.
(2014) carried out CFD simulations on a square-section angled steel lattice tower under downburst based on structured grids. Global drag coefficients of the angled steel lattice tower segment were obtained. In order to validate the rationality of the wind tunnel test models as well as the experimental drag coefficients, the third force-test segment (from top to bottom) in Fig.1 was selected for CFD simulating analysis. The FLUENT software was used for CFD analysis of the tested segment. The height of the segment is 0.22 m. The top width and the bottom width of the segment are 0.337 m and 0.353 m, respectively. The sizes and dimensions of main members, diagonal members and auxiliary members in CFD model are fully consistent with the test model. The solidity ratios of three lateral faces are equivalent and valued as 0.3. The intersection angle between the main members and the top wall as well as the bottom wall is 86°. Therefore the flow components in the direction of the top wall and the bottom wall can be ignored. According to the geometrical model, fully structured multi-block patched grids consist of 9.49 million hexahedron elements were generated. Rectangular computational region shown in Fig. 7 (a) was employed, with its velocity inlet boundary, pressure outlet boundary and lateral smooth wall boundary placed 1.1 m away from the axisymmetric axis of the tower body, and the geometrical dimensions of the computational region in length, width and height are 2.2 m, 2.2 m and 0.22 m, respectively. The top wall and the bottom wall are flush with the top and the bottom face of the tower body, respectively. The grids on model surfaces and those at three middle height sections are presented in Fig. 7(b) and (c), respectively. The employed boundary conditions illustrated in Fig. 7(a) are velocity inlet (u¼ 30 m/s, v ¼w¼ 0), non-slip adiabatic wall boundary for section model of tower body, free-slip adiabatic wall for bottom wall, ceiling wall, sidewall, respectively, and back pressure is set for outlet boundary. The back pressure at pressure outlet boundary was set to be standard atmosphere pressure (1.01325 105 Pa). In order to well capture the flow characteristics in the near-wall zone, the shear stress transport (SST) k-ω
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97
Fig. 5. Definition of the coordinate system and the wind incidence angle.
Table 2 Illustrations on the wind tunnel test cases. Case number
Face A
Face B
Face C
V(m/s)
θ(°)
1 2 3 4 5 6 7 8 9
ϕ1 ϕ2 ϕ3 ϕ1 ϕ1 ϕ2 ϕ1 ϕ2 ϕ3
ϕ1 ϕ2 ϕ3 ϕ2 ϕ3 ϕ3 / / /
ϕ1 ϕ2 ϕ3 ϕ2 ϕ3 ϕ3 / / /
20 20, 30 20 20 20 20 20 20 20
0 180° 0 180° 0 180° 0 180° 0 180° 0 180° 0 360° 0 360° 0 360°
Face B
Cross arm
Face A
Face C
Cross arm
Fig.6. Illustration of the sectional property of triangular tower body.
Fig. 4. Photos of the single frame model of face A.
turbulence model was employed. Both the inviscid and viscous terms of Navier-Stokes equations were discretized by using the second-order upwind scheme. The Standard scheme and the
SIMPLEC scheme were selected for pressure interpolation and velocity-pressure coupling, respectively. For different wind incidence angles, the surface pressures and the drag force of the tower body can be calculated by using CFD. When the wind incidence angles are θ ¼0° and 30°, the surface pressure contour of the tower body from two view angles is shown in Fig. 8. For wind incidence angle in the range of 0° r θ r60°, the drag coefficients of the triangular tower body calculated by CFD are compared with the experimental values in Table 3 with an angle interval of 10°. It can be seen that the CFD results are basically well agreed with the wind tunnel test values. The maximum relative deviation is not higher than 7%. Especially for the 0° wind incidence angle corresponding to the maximum drag coefficient, the relative variation between the CFD analysis value and the experimental value is only about 0.9%. On this point, a conclusion on the rationality of the wind test model as well as the experimental results can be made. In Table 3, it can also be found that the minimum drag coefficient appears when the wind incidence angle falls in the range from 30° to 40°, resulting in minimum global wind loads acting on the triangular tower segment.
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Velocity inlet
Pressure outlet
2.2m
0.22m 0.11m
Middle height section
2.2m
0.22m Bottom wall Side wall
Section model of tower body
Fig. 7. Grids of the segment model.
3.3. Experimental results and discussion 3.3.1. Global drag coefficients As discussed in Section 3.1, the global drag coefficients of the triangular tower body in wind directional axis can be calculated according to Eq. (2). The global drag coefficient curves for Case 2 under the mean wind speed of V¼20 m/s and V ¼30 m/s are plotted in Fig. 9(a). By considering that the separation points of the air flow passing through angle section members are fixed, the Reynolds number effects on the aerodynamic characteristics of angle section members can be ignored. Therefore the global drag coefficients of the angled steel triangular tower body do not differ significantly at two different mean wind speeds. At the case of the wind incidence angle θ ¼ 120°, the maximum difference between the global drag coefficients under V ¼20 m/s and V ¼30 m/s is only about 4.4%. When the mean wind speed is 20 m/s, the radar graph of the drag coefficients in wind directional axis is plotted as shown in Fig. 9(b). For the equilateral triangular tower body with an
Fig. 8. Pressure contour of the tower body (Unit: Pa). Table 3 Comparison on the drag coefficients by CFD analysis and wind tunnel test. θ(°)
0
10
20
30
40
50
60
Experimental values CFD analysis values
2.15 2.13
2.08 2.05
1.91 1.87
1.72 1.69
1.67 1.70
1.72 1.83
1.74 1.86
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identical solidity ratio of three lateral faces, Fig. 9(b) shows that the global drag coefficient curve is approximately symmetrical to the axis of θ ¼60°. It can be observed that the drag coefficients at the symmetrical wind incidence angles are slightly different. Example for a symmetrical pair of θ ¼30° and θ ¼90°, the corresponding drag coefficient in wind directional axis is 1.71 and 1.68 respectively. The slight differences between the drag coefficient at angles of attack 30° and 90° are attributed to differences in the orientation of the 60° angled steel main members, 90° angled steel diagonal members and auxiliary members (Simon Prud’homme et al., 2014). This similar conclusion can also be verified by the research of Mara and Galsworthy (2011). When the solidity ratios are 0.2 and 0.3, the drag coefficient curves of the triangular tower bodies are presented in Fig. 9(c). It can be seen that the drag coefficient in wind directional axis decrease with the increasing of the solidity ratio, while the varying trends depending on the wind incidence angle are generally consistent. The calculation methods of the drag coefficients of triangular lattice towers are regulated in some standards including ASCE standard (1991, 2010), British standard, Australia/New Zealand structural design standard and Chinese structural design standard. The proposed drag coefficients are generally corresponding to the 0° wind incidence angle. For Case 1, Case 2 and Case 3 of the wind tunnel tests listed in Table 2, the experimental values of the global drag coefficient in wind directional axis are compared with the calculated values by some design standards in Fig. 10. It can be seen that the experimental values are more close to the values calculated by British standard. When the solidity ratios of the lateral faces are 0.2, 0.3 and 0.4, the calculated drag coefficients are higher than the experimental values by 2.0%, 6.9% and 4.7% respectively. The drag coefficients calculated by Chinese structural design standard are all lower than the experimental values. It indicates that the wind loads acting on triangular towers will be underestimated by employing Chinese structural design standard. 3.3.2. Skewed wind load factors By considering the relative intersection angle between the electrical lines and the transmission tower structures, the 0°, 30°, 45° and 90° wind load case usually should be considered in the structural design of transmission towers. The skewed wind load factor Kθ is an important parameter for calculating the skewed wind loads on transmission towers (Mara and Ho, 2011; Yang et al., 2015). All the wind tunnel tests in this study were completed under steady-state flow conditions. The test models are rigid enough to ensure that a slight turbulence effect (the turbulence
Fig. 9. Drag coefficients in wind directional axis.
Fig. 10. Comparison on the drag coefficients.
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intensity is within 0.2%) of the wind flow on the drag force can be neglected. The wind loads of transmission tower bodies under skewed wind in ASCE standard, IEC standard and European standard etc. are calculated by:
FDθ =
1 2 ρV CD Ab Kθ 2
(3)
where FDθ is the measured drag force when the wind incidence angle is θ, CD is the drag coefficient when the wind incidence angle is 0°, Ab is the total projected area of the members belong to Face A in Fig. 5. The skewed wind load factor can be calculated by Kθ = CDθ /CD . Only the British standard proposes specific method for calculating the skewed wind load factor of triangular tower bodies. In particularly, the calculation formula of Kθ for the equilateral triangular section tower body with three equivalent lateral faces is as follows:
Kθ =
Abf ⎡ Abc + ⎣ 1 − 0.1 sin2 ( 1.5θ ) ⎤⎦ Ab Ab
(4)
where Abc is the total projected area of the tubular section members, Abf is the total projected area of the angle section members. Especially for the triangular tower bodies fully made of angle section members, Eq. (4) can be simplified as Kθ = ⎡⎣ 1 − 0.1 sin2 ( 1.5θ ) ⎤⎦. For an equilateral triangular section tower body, in a symmetrical period of the wind incidence angle θ from 0° to 120°, the experimental curves of skewed wind load factor Kθ for Case 1 and Case 2 are presented in Fig. 11. It can be seen that the skewed wind load factor calculated by British standard is generally higher than the experimental values. The Kθ curve in British standard is symmetrical to the axis of θ ¼60° and Kθ is decreased to its minimum value when the wind incidence angle is 60°. The experimental curves of the skewed wind load factor Kθ approximately appear like W shape and symmetrical to the axis of θ ¼60°. However Kθ is decreased to its local minimum value when the wind incidence angle is 40° or 80°. In other words, the wind loads acting on the triangular tower body is decreased to the minimum value for these incidence angles. This conclusion can also be validated by the CFD analysis results in Table 3 in Section 3.2. For the convenience of comparing with experimental results and calculated values by British standard, the wind incidence angle of 0°, 30° and 60° in the study by Mara and Galsworthy (2011) can be equivalently transformed to 60°, 30° and 0° as defined in Fig. 5. The wind tunnel test results presented in this study also indicate that the wind
Fig. 11. Comparison of the skewed wind load factors (Face A is equivalent to face B and face C).
incidence angle corresponding to the minimum wind loads acting on a triangular tower body is 30°. Besides the Kθ values calculated by British standard are higher than the experimental values, the shape and the lowest position of the Kθ curve in British standard are different from the experimental curves. It demonstrates that the skewed wind load factor calculated by British standard for some wind incidence angles may be oversimplified and inaccurate. The calculation formula such as Eq. (4) given by British standard should be improved. When the solidity ratio of face A is different from the other two faces (example for Case 4, Case 5 and Case 6), the skewed wind load factor Kθ for θ in the range from 0° to 120° is defined as:
⎧ CDθ (0o ≤ θ < 60o) ⎪ ⎪ CDA ⎪ 2CDθ (θ = 60o) Kθ = ⎨ C ( ⎪ DA + CDB ) ⎪ CDθ ⎪ (60o < θ ≤ 120o) ⎪ ⎩ CDB
(5)
where CDA, CDB are the global drag coefficients of triangular tower bodies when θ ¼0° and θ ¼120°, respectively. According to Eq. (5), the skewed wind load factor Kθ for Case 4, Case 5 and Case 6 can be calculated and compared with British standard in Fig. 12. Fig. 12 shows that the experimental curves of the skewed wind load factor Kθ still approximately appear like W shape. The symmetry axis of the skewed wind load factor Kθ is shifted near to θ ¼50°. Kθ is decreased to its local minimum value when the wind incidence angle θ is 30° or 70°. The varying trend of Kθ , especially for the wind incidence angle corresponding to the minimum value in British standard, are significantly different from experimental results. The skewed wind load factors calculated by British standard are generally higher than the experimental values. Only when the wind incidence angle is in the range of 50° to 60° for Case 4 and Case 5, the experimental values are higher than the calculated values according to British standard. In these cases, the wind loads acting on triangular tower bodies would be underestimated by employing British standard. 3.3.3. Shielding factors In British standard and Chinese standard, the global drag coefficients of lattice tower bodies can be derived from the drag coefficient of the windward face by considering the effective shielding effect on leeward faces. Comparing to square and
Fig. 12. Comparison of the skewed wind load factors (Face A is different from face B and face C).
F. Yang et al. / J. Wind Eng. Ind. Aerodyn. 156 (2016) 93–103
rectangular-section tower structures, the shielding effect of triangular section tower structures has special characteristics. If face A in Fig. 5 is assumed as the windward face, face B and face C are both leeward faces. The shielding factor of triangular tower should be specially studied. The drag coefficient of face A can be measured by the test model shown in Fig. 4. And based on the global drag coefficient of triangular tower bodies for Case 1, Case 2 and Case 3, the shielding effect of face A on face B and face C were analyzed. The global wind load of a triangular tower body consists of three wind load components acting on three lateral faces. The global wind load on a triangular tower body can be written as:
FWT = FSA + FSB + FSC
(6)
where FWT is the global wind load of a triangular tower body, FSA, FSB and FSC are the wind load acting on the lateral face A, face B and face C respectively. When the wind direction is normal to a lateral face and the wind load acting on this face is FS. For the ith acute angle θi between the wind direction and the lateral face, the wind load acting on this lateral face can be calculated by:
(7)
Fi = FS sin θi
As discussed on triangular tower structures above, the wind loads acting on two leeward faces will be reduced for the shielding effect induced by the windward face. If the wind load acting on face A in Fig. 5 is selected as a reference parameter, Eq. (6) can be written as:
FWT = FSA (sin θiA + ηB sin θiB + ηC sin θiC )
(8)
where ηB and ηC are the shielding factor of face B and face C, respectively. According to Eq. (1), Eq. (8) can be converted to a dimensionless form by employing the item of drag coefficients, and the new expression is given as:
CD = CDA (sin θiA + ηB sin θiB + ηC sin θiC )
(9)
The global drag coefficient of the triangular tower body equals to the maximum value when the wind incidence angle is 0° or 120°. For the convenient use in design process, the drag coefficient under the wind incidence angle θ ¼0° is employed to calculate the shielding factor. Then the global drag coefficient of the triangular tower body can be calculated by:
CD = CDA ( 1 + ηB sin 30o + ηC sin 30o)
(10)
In particularly, for an equilateral triangular section tower body, it can be defined as ηB ¼ ηC ¼ η. The calculation formula of the shielding factor can be written as:
η=
CD −1 CDA
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Table 5 Comparison of the shielding factor η.
ϕ
C¯D
C¯DA
η
0.2 0.3 0.4
2.449 2.080 1.878
1.602 1.384 1.355
0.53 0.50 0.39
θ ¼ 120° and the drag coefficient CDA for θ ¼360° should be fully agreed with the corresponding values for θ ¼ 0°. However, the experimental errors induced by measuring apparatus and model making, can not be fully avoided. Therefore the drag coefficients at corresponding wind incidence angles exhibit slight differences. In order to improve the accuracy of experimental data, the drag coefficients at two corresponding wind incidence angles were averaged. The average value of the global drag coefficient and the drag coefficient of single lateral faces are expressed by C¯D and C¯DA . According to Eq. (11), the shielding factor η can be calculated and listed in Table 5. In British standard, the drag coefficients for single lattice frames made by angle section members, Cnf , is given by:
⎧ 1.8 ϕ ≤ 0.6 ⎪ 1.58 + 1.05 ( 0.6 − ϕ) Cnf = ⎨ 2 ⎪ ⎩ 1.58 + 2.625 ( ϕ − 0.6) ϕ > 0.6
When the solidity ratio ϕ are 0.2, 0.3 and 0.4, the drag coefficient of face A calculated by Eq. (12) are 1.78, 1.70 and 1.64 respectively. The calculated drag coefficients by British standard are higher than the experimental values in Table 5 by 11.1%, 22.8% and 21.0%. In the applicable standards, only the British standard proposes the calculation method of the shielding factors for triangular towers. For the triangular towers fully making by angle section members, the calculation formula of the shielding factor is given by:
η=
2 ( 1 − ϕ)1.89 3
When the wind incidence angle θ ¼ 0°, 120° or 360°, the global drag coefficient CD and the drag coefficient CDA are listed in Table 4. In purely theoretical point, the global drag coefficient CD for Table 4 Drag coefficients of the tower body and the single frame for θ ¼0°. θ(°)
CD
θ(°)
CDA
0.2
0 120
2.409 2.488
0 360
1.669 1.534
0.3
0 120
2.096 2.063
0 360
1.431 1.338
0.4
0 120
1.839 1.917
0 360
1.379 1.331
(13)
In Fig. 13, the experimental shielding factors of triangular tower bodies are compared with the calculated values by Eq. (13) regulated in British standard. When the solidity ratio ϕ are 0.2, 0.3 and 0.4 respectively, the calculated shielding factors by British standard are lower than the experimental values by 17.5%, 32.1% and 34.9%. If it was assumed that the drag coefficients for single lattice frames calculated by Eq. (12) are equivalent to the experimental
(11)
ϕ
(12)
Fig. 13. Comparison on the shielding factors η.
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5. Conclusions and recommendations
Table 6 Comparison on the effective projected areas. Experimental values(m2) Calculated values(m2) Relative variations (%)
Case number
θ(°)
4
0 0.371 120 0.408
0.383 0.444
3.2 8.9
5
0 0.416 120 0.480
0.427 0.495
2.7 3.2
6
0 0.453 120 0.560
0.482 0.508
6.3 9.2
A series of wind tunnel tests on 1:7 scaled body models and single frame models of a triangular transmission tower made by angled steel members were carried out. Under different wind incidence angles, the drag coefficients of the total tower body or single frames with three solidity ratios for nine test cases were obtained. The experimental results from wind tunnel tests were also mutually validated by CFD analysis. The design parameters including the drag coefficient, the shielding factor as well as the skewed wind load factor were analyzed. The main findings are summarized as follows:
For the equilateral triangular tower body with an identical so-
values, the global wind loads acting on triangular tower bodies would be underestimated by British standard. Based on the above analysis, the drag coefficients of single lattice frames calculated by British standard are lower than the experimental values, and the shielding factors are in a reverse turn. While the increasing extents of the shielding factors are higher than the decreasing extents of the drag coefficients of single lattice frames, it can be concluded that the global drag coefficients calculated by British standard are higher than the experimental values according to Eq. (9). This conclusion can also be verified by the comparison analysis in Fig.10.
4. Additional results-application on effective projected areas When the solidity ratio of face A is different from the other two faces, the projected areas of the members of windward faces are not identical for calculating the global drag coefficients under different wind directions. Therefore it is difficult to calculate the global drag coefficients by the drag coefficients of single lateral faces. The parameter CD Ap which usually called effective projected area (EPA) was proposed and employed to evaluate the wind loads acting on triangular towers with three different lateral faces. According to the Eq. (4), (Eq. (6) and 7), when the wind incidence angle θ ¼0° and θ ¼120°, the effective projected areas of the triangular tower bodies can be given as:
( CD Ap )θ= 0o = CDA ApA + ( CD Ap )θ= 120o = CDB ApB
ηA ( CDB ApB + CDC ApC ) 2 ηB + ( CDC ApC + CDA ApA ) 2
lidity ratio for three lateral faces, the global drag coefficient curve is approximately symmetrical to the axis of θ ¼60°. When the wind incidence angle is 0°, the experimental drag coefficients are more close to the calculated values by British standard. When the solidity ratios of the lateral faces are 0.2, 0.3 and 0.4, the calculated drag coefficient are higher than the experimental values by 2.0%, 6.9% and 4.7% respectively. The wind loads acting on triangular towers will be underestimated by Chinese structural design standard. For the equilateral triangular tower body with an identical solidity ratio for three lateral faces, the experimental curves of the skewed wind load factor Kθ approximately appear like W shape and symmetrical to the axis of θ ¼ 60°. Kθ is decreased to its local minimum value when the wind incidence angle is 40° or 80°. When the solidity ratio of face A is different from the other two faces, the symmetry axis of Kθ is shifted to θ ¼50°. Kθ is decreased to its minimum value when the wind incidence angle is 30° or 70°. The varying trend of Kθ , especially for the wind incidence angle corresponding to the minimum value in British standard, are quite different from experimental results. When the wind incidence angle is in the range of 50° to 60° for some test cases, the wind loads acting on triangular tower bodies would be underestimated by employing British standard. Based on a combination of the drag coefficient of single frames and the shielding effect factor, a calculation method of the effective projected areas for triangular tower bodies was proposed. When the wind incidence angle θ is 0° or 120°, the calculated values of the effective projected areas agree well with the experimental values by the total tower-body models.
(14)
where CDA, CDB and CDC are the drag coefficients of the single lateral face A, face B and face C, ηB and ηC are the shielding factor of face B and face C respectively, and these five parameters can be valued according to Table 5. ApA, ApB and ApC are the projected areas of the single lateral face A, face B and face C respectively. When the solidity ratios are 0.2, 0.3 and 0.4, the corresponding projected areas are 0.137 m2, 0.205 m2 and 0.372 m2 respectively. At the case of the wind incidence angle is θ ¼0° or θ ¼120°, the effective projected areas determined by the wind tunnel tests on global models as well as the calculated values by Eq. (14) are listed in Table 6. By employing the drag coefficients of single lateral faces and the shielding factors η, the effective projected areas calculated by Eq. (14) are generally agreed well with the experimental values by global test models. The relative variations are in a range from 9.2% to 2.7%. It indicates that Eq. (14) is suitable for calculating the global wind loads on triangular tower bodies. Except for θ ¼120° under Case 6, the calculated effective projected areas are higher than the experimental values. The global wind loads acting on triangular tower bodies calculated by Eq. (14) are generally conservative and may induce more safe design.
Acknowledgements This work has been funded by the financial support from National Natural Science Foundation of China (51408568, 51308519) and State Grid Corporation of China. The authors would like to thank the sponsors.
References Akira Hayakawa, Takeshi Ohkuma, Kazutsugu Hiramatsu, et al., 2003. Characteristics of wind forces on a triangular telecommunications steel tower. 11th International Conference on Wind Engineering, IAWE, Texas, USA. American Society of Civil Engineers (ASCE), 1991. ASCE manuals and reports on engineering practice No.74. Reston, American. American Society of Civil Engineers (ASCE), 2010. ASCE manuals and reports on engineering practice No.74. Reston, American. AS/NZS 1170.2, 2011. Structural Design Actions: Part 2-Wind actions. Standards Australia Limited/Standards New Zealand, Sydney, Australian. AS/NZS 7000, 2010. Overhead line design-Detailed procedures. Standards Australia Limited/Standards New Zealand, Sydney, Australian. BS-8100, 1986. Lattice tower and masts-Part1: Code of practice for loading. British Standards Institution, London, Britain.
F. Yang et al. / J. Wind Eng. Ind. Aerodyn. 156 (2016) 93–103
DL/T 5154-2012, 2012. Technical code for the design of tower and pole structures of overhead transmission lines. China Planning Press, Beijing, China, in Chinese. EN 50341-50341, 2012. Overhead electrical lines exceeding AC 1kV-Part 1: General requirement—common specifications. European Committee for Electrotechnical Standardization, Brussels, Belgium. GB 50009-52012, 2012. Load code for the design of building structures. China Architecture and Building Press, Beijing, China, in Chinese. Georgakis, C.T., Støttrup-Andersen, U., Johnsen, M., et al., 2011. Drag coefficients of lattice masts from full-scale wind-tunnel tests. 5th European and African Conference on Wind Engineering, Florence, Italy. Holmes, J.D., 2008. Recent developments in the specification of wind loads on transmission lines. J. Wind Eng. 5 (1), 8–18. IEC 60826, 2003. Design criteria of overhead transmission lines. International Electrotechnical Commission, Geneva, Switzerland. JEC-127-1979, 1979. Design Standards on Structures for Transmissions. Japanese Electrotechnical Committee, Tokyo, Japan, in Japanese. Mara, T.G., Ho, T.C.E., 2011. Design loads for transmission towers under skewed wind loading. Struct. Congr. 2011 © ASCE 2011, 1246–1257. Mara, T.G., Galsworthy, J.K., 2011. Comparison of model-scale and full-scale wind
103
tunnel test results for a typical 3-dimensional lattice frame. 13th International Conference on Wind Engineering, Amsterdam, NL. Prud’homme, Simon, Legeron, Frederic, Laneville, Andre, et al., 2014. Wind forces on single and shielded angle members in lattice structures. J. Wind Eng. Ind. Aerodyn. 124, 20–28. Whitbread, R.E., 1977. Wind Loading on Lattice Towers, Report on Project Number P352003, National Maritime Institute, UK. Xie, H.P., He, M.J., Ma, R.L., 2010. Analysis of mean wind load of lattice tower based on CFD simulation. J. Cent. South Univ. (Sci. Technol.) 41 (5), 1980–1986, in Chinese. Xie, Q., Zhang, Y., Li, J., 2006. Investigation on tower collapses of 500kV RenShang 5237 transmission line caused by downburst. Power Syst. Technol. 30 (10), 59–63, in Chinese. Yang, Fengli, Yang, Jingbo, Niu, Huawei, et al., 2015. Design wind loads for tubularangle steel cross-arms of transmission towers under skewed wind loading. J. Wind Eng. Ind. Aerodyn. 140, 10–18. Zhang, L., Li, J., Dang, H.X., 2014. Investigation of wind loads of lattice tower in downburst. Chinese. J. Appl. Mech. 31 (3), 343–347, in Chinese.